Season brisket with salt and pepper. In a large skillet, pot, or stainless steel roasting pan over medium-high heat, add oil, and heat until shimmering. Add brisket and brown on both sides, about 6 minutes per side. Transfer brisket to a work surface.
Add onion, carrot, celery and garlic to pan and cook, stirring, until just starting to brown in spots, about 6 minutes; season with salt. Add wine and bring to a simmer while scraping up browned bits from bottom of pan. Stir in ketchup and tomatoes and return brisket to roasting pan, nestling it among vegetables.
Add thyme and bay leaves to roasting pan and cover well with foil. Set oven to 300 degrees F and cook brisket on middle rack until fork-tender, 3 to 4 hours.
Transfer brisket to a work surface and let rest 30 minutes. Skim fat from surface of braising liquid and season liquid with salt and pepper; discard thyme sprigs and bay leaves. Slice brisket thinly against the grain, then transfer back to braising liquid, making sure to submerge slices well. Cover and let stand for 30 minutes in a warm place. Serve.