Heat oil in a large pot over medium heat.
Add onions and garlic, cooking until softened. Stir in paprika, salt, and pepper.
Add chicken pieces to the pot, browning on all sides.
Pour in chicken broth and bring to a boil. Reduce heat to low, cover, and simmer for about 45 minutes, or until chicken is cooked through.
Remove chicken from the pot and stir in sour cream to the liquid to make the sauce.
Return chicken to the pot to warm through.
For the dumplings, mix flour, eggs, water, and salt in a bowl until a sticky dough forms.
Drop teaspoonfuls of dough into boiling salted water.
Cook until they rise to the surface, then remove with a slotted spoon.
Serve chicken and sauce over dumplings, garnished with additional sour cream if desired.
