On top of the stove, heat oil in the bottom of a heavy Dutch oven until it almost smokes. Season the brisket with salt and pepper. Carefully lay brisket in pot, fat side down. When browned, flip over.
Cut garlic head in half across the cloves. Chop onion, celery and carrots into 2" pieces. Tie thyme, rosemary, parsley and bay leaf together with cotton twine to form a bouquet garni.
When brisket is browned, remove meat to a plate. Put the onion, garlic, celery, carrot and bouquet garni into the pot and allow to caramelize and cook down, approximately 10-15 minutes.
Add tomatoes, beef broth and red wine to pot. Stir well, scraping up any browned bits at the bottom of the pot. Return meat and any accumulated juices to the pot. Cover tightly and place in a preheated 325 degrees F oven for 2 hours.
Remove brisket from pot to a platter. Let rest 10 minutes.
Slice across the grain. Return sliced meat to the pan and continue cooking for 1 hour.
Strain the juices from the pot, discarding the solids, and serve alongside the meat.