1. Preheat oven to 300 degrees. Generously season brisket with salt and pepper. Heat 2 tablespoons oil in a large Dutch oven over medium-high. Sear brisket until browned, 4 to 5 minutes a side; transfer to a plate. Drain fat from pot and discard. Reduce heat to medium; add remaining 2 tablespoons oil, shallots, garlic, and potato starch and cook, stirring, 2 minutes. Stir in wine, scraping up any browned bits from bottom of pot. Add broth, mustard, zest, and thyme; bring to a boil. Add meat and any accumulated juices. Cover and transfer to oven; cook 2 hours, 15 minutes.

2. Flip meat over; add vegetables. Cover and continue to cook until everything is very tender, about 45 minutes. (If you're saving it for the next day, let cool, then cover and refrigerate overnight. Reheat, covered, in a 350 degrees oven until warmed through, about 40 minutes.)

3. Transfer vegetables to a platter and meat to a cutting board; season with salt. Skim fat from liquid in pot. Stir in lemon juice; season with salt and pepper. Slice brisket against the grain and serve, with vegetables and sauce.