01 - Set the oven to 320°F (160°C) to prepare for braising.
02 - Pat the beef brisket dry. Rub evenly with olive oil, kosher salt, black pepper, smoked paprika, and brown sugar.
03 - Heat a large Dutch oven over medium-high heat. Sear the brisket on all sides until well browned, approximately 3 to 4 minutes per side. Remove and set aside.
04 - In the same pot, add onions, carrots, celery, and garlic. Cook for 4 to 5 minutes, stirring occasionally, until softened.
05 - Incorporate bay leaves and dried thyme, then pour in the beef stock, crushed tomatoes, and red wine. Stir to combine thoroughly.
06 - Return the brisket to the pot, submerging it in the liquid. Bring to a gentle simmer, cover, and transfer to the oven. Braise for 3 hours, turning the brisket halfway through, until fork-tender.
07 - Place sweet potatoes in a large saucepan, cover with cold water, add a pinch of salt, and bring to a boil. Simmer until very tender, about 15 to 20 minutes. Drain thoroughly.
08 - Return the drained sweet potatoes to the pot. Mash with unsalted butter, milk or plant-based alternative, and season with salt and pepper until creamy and smooth. Keep warm.
09 - Remove brisket from the oven and allow it to rest for 10 minutes. Skim excess fat from the braising liquid and discard bay leaves. Slice brisket thinly against the grain.
10 - Arrange slices of brisket atop the sweet potato mash. Spoon the braising sauce and softened vegetables generously over the top before serving.