To prepare drunken meat balls, soak bread crumbs in milk until thoroughly moistened; squeeze dry with hands. Combine bread crumbs, ground beef, ground pork or veal, eggs, shallots, parsley, salt, pepper and nutmeg in medium bowl. Form mixture into 6 to 8 balls or patties (2 inches in diameter and 1/2-inch thick); dust with 2 Tablespoons flour.
Heat butter and oil in deep, heavy Dutch oven, until hot but not smoking, over high heat. Add drunken meat balls; cook until browned on all sides, about 5 minutes, making sure butter does not burn. Remove meat balls to platter; keep warm.
To prepare sauce, discard all but 2 tablespoons of fat in pan. Add onion and endives. Cook over low heat, stirring constantly, for about 10 minutes. Add sugar, salt, pepper and 2 tablespoons flour to vegetables; cook, stirring, for 1 to 2 minutes longer. Add beer and broth; heat to quick boil, scraping up all brown bits from bottom of pan.
Reduce heat to simmer; return meatballs to pan, placing them on top of vegetables.
Simmer, partly covered, until meat is cooked through, 45 minutes. Sprinkle with parsley and serve.