The sauce preparation begins by melting butter in a large skillet over medium-high heat. The chicken is then added and cooked until it attains a light brown color, typically within 3 to 5 minutes per side. To enhance the flavors, onions are included and cooked until they become translucent, which usually takes around 5 to 8 minutes.
Water is poured into the skillet and seasoned with paprika, pepper, and salt. The cooking process continues until the chicken is thoroughly cooked, indicated by its lack of pinkness at the bone and clear juices. This typically takes an additional 10 to 15 minutes. To ensure it's fully done, an instant-read thermometer can be used near the bone, which should display a minimum temperature of 165 degrees F (74 degrees C). Once cooked, the chicken is removed from the skillet and kept warm.
As the chicken cooks, a large pot of water should be brought to a boil over high heat.
To make the dumplings, begin by mixing water, eggs, and salt together in a large bowl. Gradually stir in flour until a stiff batter forms. Then, using spoons, scoop up some batter and carefully drop it into the boiling water. Repeat this step until several dumplings are cooking. Allow them to cook for approximately 10 minutes or until they float to the top. Once done, use a slotted spoon to remove the dumplings from the water and let them drain in a colander or sieve. Rinse them with warm water before draining again. Repeat this process to make the remaining dumplings.
To complete the sauce, combine sour cream and flour in a small bowl. Stir until thoroughly mixed. Gently incorporate this mixture into the skillet with the sauce. Gradually bring the sauce to a boil, ensuring constant stirring, and continue cooking for approximately 2 to 3 minutes until it thickens.
The dumplings are gently spooned into the sauce and stirred until coated. They are cooked until heated through, typically for about 2 to 3 minutes. Finally, the dumplings, sauce, and chicken are spooned onto serving plates.