Sprinkle the short ribs evenly with the salt and pepper.
Heat a very large Dutch oven (I use my 9-quart Le Creuset) over medium-high on the stovetop.
In uncrowded batches, add the short rib and brown thoroughly on all sides. Remove to a plate.
If there is more than about two tablespoons of fat in the pan, remove it. Reduce heat to medium.
Preheat oven to 325°F with a rack in the lower third.
Add onion, carrot, and celery to the pot and stir to coat with the fat.
Cook, stirring occasionally, until the vegetables have released the browned bits from the bottom of the pan and are starting to soften.
Add the garlic and tomato paste and cook, stirring, for one minute.
Pour in the wine and the broth and add the herbes de Provence and the bay leaves.
Bring to a boil.
Add the meat and any accumulated juices back to the pan, nestling it in so it's covered as much as possible by the liquid.
Cover and transfer to the oven to cook for about three hours, until meat is fork-tender and easily falls off the bone.
If possible, at this stage I like to let the whole thing cool and refrigerate it overnight. This allows much of the substantial fat content of the sauce to rise to the surface and solidify, making it easy to remove. The dish will still be amply rich, but the sauce won't be greasy. If you don't have time for this step, skim off as much of the liquid fat from the sauce as possible before proceeding.
Remove beef from pot and set aside. It's traditional to make an attempt to keep the bones loosely attached to the meat for serving, but I find they often fall off. When this happens I remove and discard the bones, and no one minds. You can choose what to do.
Remove and discard bay leaves.
Place the flour into a small mixing bowl. Spoon out enough of the sauce to mix with the flour and create a smooth paste.
Place the pot over medium-high heat on the stovetop. Whisk in the flour mixture.
Bring sauce to a boil, reduce heat, and simmer for about five minutes, until thickened.
Return beef to pot to coat with sauce.