Season meat with salt and pepper. Heat oil in a large skillet over medium-high heat. Add deer and brown evenly until meat is rare. Remove meat from skillet. Add next 3 ingredients and sauté for 2 minutes. Stir in remaining ingredients and cook while stirring until smooth, about 2 minutes more. Reduce heat to low. Slice meat across the “grain” into 1/2-inch thick medallions. Return sliced meat to pan and heat through, but not beyond medium-rare. Serve with steamed rice.