Peel and thinly slice onions. Set aside. In a dinner plate, combine flour with the garlic powder, 1/3 teaspoon paprika and 1/8 teaspoon each of salt and pepper.
Skin chicken (use a paper towel to grasp the skin and pull it off.) Pat chicken dry with paper towels. Set up an assembly line from left to right with the chicken, the seasoned flour, and a 9x13 pan. Using a fork, dredge each piece of chicken in the flour on both sides and place the floured chicken in the pan.
In your largest skillet, heat the olive oil on medium high. Add the onions and cook them for six minutes or until they are soft, stirring occasionally.
Add the chicken to the skillet with the onions and brown the meat on both sides, for a total of 7-10 minutes. (You can do this in batches if needed or use a second skillet to brown some of the chicken in a bit of olive oil.)
While the chicken is browning, whisk 1 tablespoon paprika into 1 1/2 cups of chicken stock. Place all of the browned chicken in the large skillet with the onions, and pour the seasoned chicken stock over it. Lower the heat to medium and cover the pan. Simmer for at least 25 minutes. (Check on it once during that time, to spoon some gravy over the chicken.)
While the chicken is simmering, prepare the dumplings. Fill a pasta pot just over halfway with hot water. Add a teaspoon of salt to the water, cover the pot, and heat it on high. In a medium mixing bowl, beat the eggs with a fork or whisk. Using a large spoon, stir in the flour, water, and 2 teaspoons of salt until well combined. (A whisk won't work well for that.)
Place the bowl with batter near the stove, along with two regular teaspoons, a large slotted spoon, a clean 9x13 pan and a roll of foil.
When the water is boiling, uncover the pot. Scoop a teaspoon of batter, and use the other teaspoon to scrape it off over the pot, so that the batter drops into the boiling water. Continue adding teaspoons of batter to the pot in a single layer, trying not to let the dumplings touch each other. (You will need to do this in batches.)
Cook the dumplings for 3-5 minutes, depending on how firm you want them.The dumplings will float when they are almost cooked. (After the dumplings float, I usually wait a couple of minutes and then cut one open to taste it. Make sure it is cooked through. If it is too firm for your liking, cook it some more. You also can cut any large dumplings in half to finish cooking.)
Use a slotted spoon (or strainer) to remove the cooked dumplings, letting any excess water drain back into the pot. Place the drained dumplings in your clean 9x13 pan and loosely cover them with foil to keep them warm. Keep your water boiling and continue cooking and draining the dumplings in batches until all of the batter is gone.
When you are done cooking the dumplings, the chicken should be ready. Cut into a piece of chicken to make sure it is not pink inside. If the chicken is cooked, turn off the heat and add dollops of sour cream around the skillet, stirring carefully after each addition.
To thicken the gravy, add a few tablespoons of the gravy to the corn starch in a cup and whisk together. Add the corn starch mixture to the skillet and carefully stir it in. You can taste the chicken and gravy to see if additional salt and pepper are needed, or just provide extra at the table.
To serve, place a portion of dumplings in the center of each plate and top with the chicken and gravy. Add salt and/or black pepper if needed.
Store leftover dumplings in the refrigerator and use them by the end of the next day. (They will start to turn grey after that.) If you wish, you can just cook half of the dumplings and save the rest of the batter in the refrigerator to cook fresh dumplings the next day. Store any leftover chicken and gravy in the refrigerator for up to three days.
If you are making this quantity of chicken and don't have a skillet larger than 12-inches, you may want to use a second skillet, even for simmering the chicken. If so, when you are ready to simmer, put some of the onions in the second pan with some chicken and use 1 1/2 cups of stock in each pan. Cover both pans and simmer until cooked. Then, you can remove just the chicken and onions (minus the stock) from the second pan and add them to the rest of the cooked chicken before adding in the sour cream and corn starch.
This recipe makes a lot of chicken, which is great for leftovers. Sometimes, I reduce the chicken part of the recipe by half, but make the full amount of gravy and dumplings, since my family eats lots of them!