Combine beef, half of chopped onion, garlic, salt, pepper, bread crumbs, egg yolks and 1/2 cup water in a large bowl. Mix well and form into 1 inch meatballs.
Heat the oil in a large nonstick skillet over medium-high heat. Add meatballs and cook, turning often, until well browned. Drain on paper towels.
Pour off excess fat in pan, leaving about 3 Tablespoons. Add remaining onion and cook until softened, about 5 minutes. Add mushrooms and cook until the liquid they give off has evaporated, about 7 to 10 minutes.
Add sherry and increase heat to high. Boil until almost all liquid has evaporated.
Add chicken stock and bring to a boil.
Rub butter with flour in small bowl until it makes a smooth paste. Pinch off pea sized pieces of mixture and add to boiling stock mixture a bit at a time, whisking constantly, for about 3 minutes.
Add the meatballs. Stir in sour cream and dill. Season to taste with salt and pepper. Cook until meatballs are just heated through.