Remove the stems and gills from the mushrooms and clean them. Brush the outside with olive oil. Place in a baking dish, stem-side up.
Cut the tomatoes in half and place in a small mixing bowl. Add the garlic, 1 tablespoon olive oil, the vinegar, Italian seasoning, and a good pinch of salt and pepper. Toss to coat. Spoon into the mushroom caps. Bake for 10 minutes. Sprinkle on the cheese alternative and bake for another 10-15 minutes or until the cheese alternative has melted and starts to brown.