Combine beef broth, Worcestershire sauce, garlic, thyme, and rosemary in a mixing bowl.
Place the venison roast in a resealable bag or shallow dish and pour the marinade over it.
Cover and refrigerate for 4–12 hours.
Prepare the Vegetables:
Chop carrots, potatoes, onion, and celery into uniform pieces for even cooking. Set aside.
Sear the Venison:
Heat olive oil or butter in a large skillet over medium-high heat.
Remove the roast from the marinade (if used) and pat it dry with paper towels. Season generously with salt and black pepper.
Sear the roast on all sides for 2–3 minutes per side to lock in juices and create a flavorful crust.
Assemble the Dish (Choose Your Cooking Method):
Oven Method: Preheat oven to 300°F (150°C). Place the seared venison roast in a Dutch oven and surround it with vegetables. Mix beef broth, tomato paste, thyme, and rosemary in a bowl. Pour over the roast and vegetables. Cover and cook for 3–4 hours or until the meat is tender.
Slow Cooker Method: Transfer seared roast to the slow cooker and add vegetables and broth mixture. Cook on low for 6–8 hours or high for 4–5 hours.
Instant Pot Method: Place seared roast in the Instant Pot with vegetables and broth mixture. Pressure Cook on High for 60–70 minutes. Let pressure release naturally for 10 minutes before opening.
Rest and Slice:
Remove the venison roast and let it rest for 10–15 minutes to allow juices to redistribute.
Slice against the grain for maximum tenderness.
Serve with Pan Sauce:
Skim off excess fat from the cooking liquid. Simmer on the stovetop for a few minutes to thicken into a savoury sauce.
Drizzle sauce over sliced venison and vegetables before serving.