Pat brisket dry and season on all sides with salt and freshly ground black pepper. In a Dutch oven or large pot over medium-high heat, heat oil until shimmering. Brown beef on all sides until a deep brown crust develops, about 7 to 10 minutes (work in batches if necessary). Transfer beef to a slow cooker.
To the Dutch oven, add onions, carrots, celery, garlic, 1 teaspoon salt, and 1/2 teaspoon pepper and cook until the onions have softened, about 5 minutes.
Stir in tomatoes, red wine vinegar, mustard, bay leaf, rosemary, and thyme and deglaze the pan by scraping up any browned bits on the bottom. Transfer to the slow cooker with the beef.
Cover and cook until the beef is fork tender, on HIGH for 5 to 6 hours or on LOW for 8 to 10 hours. Remove brisket to a cutting board and tent with foil for 10 minutes. Slice brisket thinly across the grain, arrange a platter, and drizzle with juices from the slow cooker.