Preheat oven to 325 degrees.
Rinse venison rack well and pat dry with paper towels. Rub thoroughly with about 1-2 tablespoons of olive oil. Season with salt and pepper and set aside.
Heat remaining tablespoon of oil over high heat in a Dutch oven or other ovenproof pot until shimmering. Sprinkle flour onto both sides of the venison rack. Sear meat on both sides until browned, approximately 2-3 minutes per side. Remove from heat and set on a plate to cool slightly.
Add another tablespoon of olive oil to the pot Add carrots, leeks and mushrooms and saute until vegetables are softened, 5-6 minutes. Add garlic and saute another minute. Add broth, tomato paste, red wine, rosemary and parsley and bring to a boil. Continue cooking the sauce over high heat until reduced in half.
Add balsamic vinegar and stir to combine. Nestle venison rack into sauce and place in oven. Cook for 2 to 2.5 hours until the meat falls away easily from the bone. Serve with vegetables and sauce on the side.