Combine the chuck, the chopped onion, the garlic, salt, pepper, bread crumbs, egg yolks, and water in a large bowl. Mix well and form meatballs that measure about 1-inch in diameter. Heat the oil in a large nonstick skillet over medium-high heat. Add the meatballs and cook, shaking and turning, until well browned, about 5 minutes. Don't crowd the pan; work in batches, if necessary. Transfer to paper towels to drain.

Pour off any excess fat from the skillet, leaving 3 tablespoons in the pan and add the remaining onion. Cook, stirring often, until softened, about 5 minutes. Add the mushrooms and cook, stirring, until the liquid they give off has evaporated, 7 to 10 minutes. Pour in the sherry, increase the heat to high, and boil until almost all the liquid they give off has evaporated. Pour in the stock and bring to a boil.

Rub the butter with the flour in a small bowl until it forms a smooth paste. Pinch off pea-sized pieces and add little by little to the boiling sauce, whisking constantly for 3 minutes. Add the meatballs, stir in the dill, and sour cream, season with salt and pepper, and cook over low heat until the meatballs are just heated through. Serve hot.