Pour off any excess fat that has accumulated, leaving about 2 tablespoons of fat in the bottom of the pot. Add the chopped onion, carrot, celery and garlic, and cook over medium-low heat until the vegetables have softened, about 10 minutes. Add the wine, herbs, beef broth and diced tomatoes. Return the beef to the pot with the liquid. Bring all to a boil, stirring the bottom of the pot, scraping up any browned bits.
Cover the pot and transfer to the oven. Bake until the ribs are very tender, about 2 1/2 to 3 hours. When ribs are fork tender, remove from pot and keep lightly covered. Strain the vegetables out of the broth and discard, reserving the sauce and skimming off as much fat as possible. Return the sauce to the saucepan. You should have approximately 3 cups of sauce at this point. Bring the broth to a boil, and reduce to a simmer for about 10 to 15 minutes, until the sauce just coats the back of a spoon. You should have about 2 cups of sauce left. Taste for salt & pepper and adjust seasonings. Add ribs back to the pot, or pour sauce over the ribs on your serving platter.
* If made the day before, you can refrigerate the strained sauce, thereby making it easy to remove all the fat from the surface.