Shake chicken in a mixture of flour, salt and pepper in a plastic bag to coat well. (Save any remaining seasoned flour mixture for gravy.)
Brown chicken, part at a time, in butter or margarine and vegetable oil in a kettle or Dutch oven; remove all from kettle.
Pour off drippings, then measure 1 tablespoonful and return to kettle.
Stir in onion; saute until soft.
Stir in chicken broth or bouillon, paprika and water.
Heat, scraping brown bits from bottom, to boiling; return chicken; cover.
Simmer 30 minutes, or until chicken is tender.
Remove from broth to a shallow pan; reheat broth to boiling.
Measure saved seasoned flour, adding more flour, if needed, to make 2 tablespoons.
Blend with a small amount of water to a paste in a cup; stir into broth.
Cook, stirring constantly, until gravy thickens and boils 1 minute.
Blend sour cream and cream in a small bowl; stir into kettle; return chicken.
Reheat slowly to boiling while mixing Parsley Dumplings.
Drop dough in 8 mounds on top of chicken; cover tightly.
Cook 20 minutes. (Do not lift lid of kettle while the dumplings cook.)
Serve from kettle.