Combine meat: In a large bowl, combine ground venison, ground beef, egg, bread crumbs, onion, garlic, Worcestershire sauce, thyme, salt, and pepper. Mix well until thoroughly combined.

Form patties: Shape the meat mixture into four oval patties, about 1 inch thick.

Brown patties: Heat olive oil in a large skillet over medium-high heat. Add the patties and cook for 3-4 minutes per side, or until browned. Remove patties from skillet and set aside.

Make gravy: In the same skillet, add beef broth and red wine. Bring to a simmer and cook for 5 minutes, or until reduced by half.

Thicken gravy: Whisk in flour until smooth. Cook for 1 minute, stirring constantly.

Add mushrooms: Stir in sliced mushrooms and cook until tender, about 5 minutes.

Finish gravy: Stir in butter until melted and gravy is thickened.

Return patties: Return the patties to the skillet and simmer in the gravy for 10-15 minutes, or until cooked through.

Serve: Serve hot with mashed potatoes, roasted vegetables, or your favorite sides.

Enjoy your hearty and delicious Sharon's Salisbury Steak!