Remove stems from mushrooms. With a spoon, scrape dark brown gills away from their undersides. Be careful around the edges of the mushroom caps so that they do not get torn or broken. If they get broken, it's not big deal. It will just be a little messier when served. Preheat oven to 400 degrees. Place mushrooms on a baking sheet, top side down, and roast for 6 to 7 minutes

Heat oil in a skillet over medium heat. Add garlic, onions and sage, and cook 2 to 3 minutes. Add venison and cook until browned, about 4 to 5 minutes. Stir in tomato, and season to taste with salt and pepper.

Spoon equal portions of the venison mixture into mushrooms. Place a slice of cheese on top of each. Return to oven, and roast until cheese is melted and lightly browned.