Brown the venison: Heat the olive oil or butter in a large pot or Dutch oven over medium-high heat. Season the venison cubes with salt and pepper. Brown the venison in batches, making sure not to overcrowd the pan, about 4-5 minutes per batch. Remove the venison and set aside.

Sauté the vegetables: In the same pot, add the chopped onion, garlic, mushrooms, turnips, and carrots (if using). Sauté for 5-7 minutes, until the vegetables are softened and slightly browned.

Add the liquids and herbs: Stir in the tomato paste, followed by the beef broth and red wine (if using). Return the browned venison to the pot. Add the bay leaves, thyme, and rosemary. Bring the stew to a simmer.

Simmer the stew: Lower the heat, cover the pot, and let the stew simmer for 1.5 to 2 hours, or until the venison is tender and the flavors have melded together. Stir occasionally and adjust seasoning with salt and pepper to taste.

Serve: Remove the bay leaves before serving. Garnish the stew with freshly chopped parsley and serve hot. Pair with a side of cauliflower mash or steamed greens for a complete keto meal.