In a small, heavy skillet over medium-high heat, melt 1 tablespoon butter. Add the onions and saute, stirring often until soft, about 1 to 2 minutes. Remove from the heat and set aside.
In the large bowl of an electric mixer, combine the bread crumbs and water. Let stand until soft, about 1 to 2 minutes. Add the reserved onions along with the beef, pork, egg yolks, salt, pepper, nutmeg, and allspice. Beat on low speed until smooth. Turn the mixer to high speed and beat until the mixture is light in color and fluffy, about 10 minutes. Using 2 spoons dipped in cold water, shape the meat into 1-inch balls.
In a large skillet over medium heat, melt 4 tablespoons butter. Cook the meatballs in batches of about 15 to 20 at a time and brown on all sides. Remove with a slotted spoon and drain briefly on paper towels before removing to a warmed serving platter. Cover to keep warm. When all the meatballs are cooked, reduce the heat to low and add the flour to the skillet. Cook, stirring, until lightly browned. Slowly add the beef stock. Cook, whisking, until the gravy is thick and smooth. Strain, if desired. Pour the gravy over the meatballs and serve hot.