First off, it's pronounced pap-ri-kash. This recipe is based on a Hungarian recipe that I enjoy, but this is somewhat simplified for easy week day cooking. I probably make this on average about once a week.
The ingredients as I get them in Switzerland, substitute as appropriate for your country of residence:

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~1lb [500g] Boneless Chicken Bits [dark or white doesn't matter]
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1 can chopped Tomatoes [stewed also works]
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1/2 cup [100g] Sour Cream
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~1 lb [500g] Spätzli
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1-2 Onions
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Butter
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1-2 Tbsp Paprika Paste or 1-2 tsp Paprika [powder]
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Extras: Mushrooms, Broccoli, Cauliflower, Bacon, Red/Green Peppers, ?
A word about the ingredients. In the US, I was able to find dried Spätzli [here the spätzli is fresh] which is an adequate substitute for the Hungarian version, called Galuskas. This is the biggest time saver, to make the dumplings by hand is quite time consuming, even if it's not too difficult. Another option is to use egg noodles.

I have not seen Paprika paste in the US, and if you can't find it we'll just use Paprika in it's traditional powder form--of course, it goes without saying that the best Paprika comes from Hungry, check your labels. Both forms of Paprika come in Hot or Sweet, I use a little of both.
Step 1: Put a pot of water on to boil, we'll use it to cook the spätzli. Set the sour cream on the counter to warm to room temp. Cut the onions in half, and then slice them. I like a lot of onions, so I use 2 medium to large, but you can get away with only one. Also, any type of onion will do, red, white, or yellow. Heat some butter, maybe a tablespoon or more in a skillet over medium heat. Add the onions and cook slowly, don't allow them to get browned, cook until they are soft and translucent.

Step 2: Set aside the onions in a bowl or just push them to one side of the skillet. Add the chicken. Add more butter, if necessary to keep the chicken from sticking. Sprinkle with salt and Paprika. This is where I use Hot Paprika, but if you prefer things less spicy, just use the Sweet Paprika. You really just want to brown the chicken, this should only take a couple of minutes for each side.
Step 3: When the chicken is browned, add the canned tomatoes, 1/2 can of water, sour cream, Paprika [1-2 tbsp paste, 1-2 tsp powder], onions, and extras*. I really like a good Paprika taste, but if you add too much powder, some say it tastes chalky. Stir everything together and reduce heat to low.
Step 4: You should have a beautiful orange-red colored sauce, a little thicker than whole milk. If it's too watery, don't worry, we've got some thickening power coming with the spätzli. Just let things simmer for a few minutes while you get the spätzli ready. If you're reading the instructions all the way through before cooking, then you can be careful how much water you add in Step 3 to make sure it's not too watery. If not, lesson learned.
Step 5: Add the spätzli to the boiling water. Wait 2 minutes [or follow the directions for your version], scoop out the spätzli with a strainer or slotted spoon and add to the skillet. The water is very starchy from the dumplings and if your sauce wasn't thick enough before, just cook it a bit after the dumplings are in there and it should thicken up.
Step 6: Stir to combine. Find one of the larger chunks of chicken and cut it in half to check for doneness--it should not be pink. If it is, let it cook for another 5-10 minutes, but every time I've every checked, the chicken was done, the small pieces cook fast. I prefer to eat my Paprikas with a spoon, from a bowl, and with some nice bread to soak up the sauce, yum.
Tips and the Development of the Recipe. I really enjoy this recipe, and I cook it whenever I get a chance. I have had much practice at getting just the right result. Here are a few tips to help you get good results and to explain a little bit of how the method comes together.
Curdling. Curdling is not terrible, and mostly only noticed by perfectionists like me. This is when the sour cream curdles and you're left with small white bits floating around in your sauce. This used to happen to me all the time. The reason: the temperature difference between the sour cream and the sauce causes it to cook instantly. My method avoids this by adding the tomato sauce, water, and sour cream at the same time. It's also helpful to bring the sour cream to room temperature. The cooking process in the original recipe required tempering, which just means reducing the temperature difference, the problem with that is it recommends to cool the entire skillet, add the sour cream and then reheat--who has time for that?
Extras. Another issue with week day cooking is minimizing dishes, and unfortunately, I haven't had good results with making this a one-skillet dish. It is possible to cook the spätzli in a skillet with butter, but I have always had unsatisfactory results; the spätzli seems to soak up the butter and come out very heavy. But, you might be able to save yourself pots or pans from your side dish. You can use the pot of boiling water to quickly cook a vegetable of your choice, e.g. broccoli or cauliflower and then add it to the dish at the end. You can also cook some vege with the onions, you may have noticed that there are mushrooms in the pictures above. That's because for this rendition, I cooked up some mushrooms with the onions, peppers are also good for cooking with the onions.
Bacon was also listed in the extras section, the best way to add bacon is to cook it first, set it aside and use the bacon fat to cook the onions and the chicken. Then add the bacon back to the skillet at the same time as the tomatoes. I hesitate to call it Paprikas when using bacon, as the bacon taste overwhelms the paprika, it is more reminiscent of a sauce I had in Budapest called Bacony, that's not the correct spelling, however, as my keyboard doesn't have all the special Hungarian characters required. It may not be Paprikas, but it is fantastically delicious, I highly recommend it, especially if you can find slab bacon, just cut up into 1/4 in by 1/4 in bits before you cook it, maybe use 1/8 to 1/4 lb, or to your taste.
Paprika. I once happened to catch an episode of the Frugal Gourmet where he was making Hungarian Goulash, and he just poured the paprika in, commenting that you can never have too much paprika. I feel much the same way, but you may not, so adjust the paprika levels to your taste. Also play around with the combination of Hot and Sweet, I've made some batches with all Hot paprika and it really has some kick, which can be a nice change of pace sometimes, or maybe you prefer it that way all the time, experiment and find out.