Gather all ingredients.

Make the dumplings: Fill a large pot with water and bring to a boil over high heat. Mix water, eggs, and salt together in a large bowl.

Gradually stir in flour to make a stiff batter.

Scoop up some batter with a spoon and use another spoon to scrape it into the boiling water. Repeat until several dumplings are cooking.

Cook until dumplings float to the top, about 10 minutes. Remove with a slotted spoon and drain in a colander or sieve. Rinse with warm water and drain again. Repeat to make remaining dumplings.

Start the sauce: Melt butter in a large skillet over medium-high heat. Add chicken and cook until lightly browned, 3 to 5 minutes per side.

Add onion and cook until translucent, 5 to 8 minutes.

Pour in water and season with paprika, pepper, and salt. Continue to cook until chicken is no longer pink at the bone and the juices run clear, 10 to 15 more minutes. An instant-read thermometer inserted near the bone should read at least 165 degrees F (74 degrees C). Remove from the skillet and keep warm.

Finish the sauce: Stir sour cream and flour together in a small bowl until well combined. Add to the skillet and slowly stir to combine with the sauce. Bring to a boil, stirring constantly, and cook until thickened, 2 to 3 minutes.

Gently spoon dumplings into the sauce and stir to coat. Cook until heated through, 2 to 3 minutes.

Spoon dumplings, sauce, and chicken onto serving plates.