Step 1Bring wine, carrot, leek, onion, garlic, parsley, thyme and bay leaf to boil in wide pot. Tilt pan away from burner and carefully ignite with match. Allow alcohol to burn off, then light again. If there are no flames, alcohol is completely cooked away. Cool marinade, then pour over short ribs, seal in plastic bag and marinate in refrigerator 8 to 24 hours.
Step 2Remove meat from marinade and strain marinade into saucepan, reserving vegetables. Bring marinade to simmer and skim any impurities that rise to top. Remove from heat.
Step 3Heat 1/8 inch oil in large skillet over high heat. Season both sides of each piece of meat with salt and pepper and dust with flour, patting off excess. Place meat in hot oil and cook until well-browned on all sides (adjusting heat as necessary to keep from burning), 2 to 3 minutes on each side. Remove meat to heavy oven-proof pot or casserole big enough to hold all meat snugly in one layer.
Step 4Pour off excess oil from skillet, return to heat and cook reserved vegetables until they begin to caramelize, 3 to 4 minutes. Spread vegetables over meat in even layer and add marinade and 2 cups each of veal and chicken stock. Meat should be covered with liquid; if not, add more veal or chicken stock as necessary.
Step 5Bring liquid to simmer on stove. Press a parchment paper lid snugly over meat. Bake in 275-degree oven until meat is very tender, 3 to 4 hours.
Step 6Remove meat from pot and strain liquid into tall narrow container. Discard vegetables. Once meat has cooled slightly, it can be covered and refrigerated for up to two days.
Step 7Skim fat that rises to top of braising liquid and strain liquid several times through chinois or other fine mesh strainer, until chinois remains clean. Reserve 1/3 of braising liquid for reheating short ribs before serving, if making in advance. Transfer remaining braising liquid to saucepan and reduce to sauce consistency, about 2 cups.
Step 8If reheating short ribs, place in oven-proof casserole with reserved liquid to cover. Reheat at 300 degrees until hot through.