Remove the venison roast from the refrigerator 30 minutes before cooking to reach room temperature, pat it dry with paper towels, and trim any silvery sinew.

Combine 2 tablespoons kosher salt and 1 tablespoon freshly ground black pepper in a small bowl, then rub evenly over all sides of the roast.

Heat 3 tablespoons olive oil in a Dutch oven over medium-high heat until shimmering, then sear the roast for 3 to 4 minutes on each of two main sides and 2 minutes on the remaining sides until a deep brown crust forms.

Remove the roast to a plate, add 3 quartered onions, 4 chopped carrots, and 6 crushed garlic cloves to the pot, and sauté for 2 minutes to coat with fond.

Pour in 1 cup dry red wine, scrape up browned bits, let bubble for 1 minute, then stir in 2 cups beef broth until the liquid reaches halfway up the roast.

Tuck 2 rosemary sprigs, 3 thyme sprigs, 2 bay leaves, and 1 teaspoon Dijon mustard into the liquid around the roast, then return the roast to the pot.

Cover and braise in a preheated 325°F oven for 2½ to 3 hours, or until an instant-read thermometer inserted into the center reads 160°F to 165°F.

Transfer the roast to a cutting board, tent with foil, and rest for 10 minutes. Place the pot over medium-high heat, remove herb sprigs, and optionally puree the vegetables into the sauce with an immersion blender; simmer for 2 to 3 minutes to thicken.

Slice the venison against the grain into ½-inch thick slices, arrange on a platter, and spoon the sauce and vegetables over the top before serving.