Bourguignon is a well-known French recipe typically made with beef. I've used venison — a more flavorful, less fatty protein — but kept the cooking method the same, resulting in a healthier dish with the same warm, comforting taste.
Preheat the oven to 275 degrees.
Heat 1 tablespoon of the olive oil in a large Dutch oven or braising pot over medium-high heat. Pat the venison dry with a paper towel and place in the pot in a single layer, being careful not to overcrowd. Cook without moving until brown on one side, 2 minutes. Turn and brown the other side, 2 minutes. Remove to a bowl and set aside.
Add the remaining olive oil to the same pot. Add the carrot, onion, and garlic, and sauté until starting to brown, 1-2 minutes. Place the venison and any accumulated juices back in the pot. Season with the salt and pepper. Sprinkle in the flour and stir to coat.
Add the red wine and enough beef broth to almost cover the venison and vegetables. Stir in the tomato paste, thyme, rosemary, and bay leaf. Cover and place in the oven until the venison is fork-tender and almost falling apart, about 4 hours.
Remove from the oven and discard the bay leaf. Ladle into bowls and serve.