Combine the chuck, half of 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.
Recipe courtesy Sara Moulton, Sara Moulton Cooks at Home, Broadway Books, 2002