Pre-heat oven to 350 degrees. In an enameled cast-iron casserole, heat vegetable oil. Season short ribs liberally with salt and pepper, cook on all sides over medium high heat until browned, about 2 minutes on each side. Transfer ribs to bowl and set aside.
Add chopped onions, celery, and carrots to the casserole and cook over moderate heat until softened, stirring occasionally, about 5 minutes. Add flour and tomato paste, stirring frequently until well combined and deep red, about 2-3 minutes. Stir in wine, then add ribs back into pot. Bring to a boil, and simmer for about 25 minutes until the wine is reduced by half.
Add all of the herbs, stock and whole cloves of garlic to the pot, stir. Bring to a boil again, then cover and transfer to the oven.
Braise in the oven for 2-2.5 hours, until the meat is falling off the bone, turning once halfway through.
Remove from oven, transfer ribs to a bowl. Strain braising liquid into a large skillet and boil until the liquid is reduced by half, about 15 minutes.
Put short ribs into a bowl with your favorite side dish, and spoon reduced sauce over the meat.