Heat the olive oil over medium-high heat in a saute pan. Add the tomatoes (make sure they're not wet or the oil will splatter!), salt, and a generous pinch of fresh ground pepper.
Saute the tomatoes for about 5 minutes, until they turn brown in spots and start to blister. Pierce a few of them with a sharp knife so they give off some juice. Cover the pan and let the tomatoes cook for about 10 more minutes.
When the tomatoes start to soften, add the garlic and about half of the sliced basil, and stir to combine. Reduce the heat to low, cover the pan, and let the tomatoes cook for another 5 minutes or until they're soft and most have popped open.
Meanwhile, heat the oven to 350 degrees.
Spray a baking dish or pan with oil and place the mushroom caps with the gill side facing up.
Divide the tomato mixture among the 4 mushroom caps. If there are extra tomatoes, spoon them around the mushrooms.
Place 4 pieces of mozzarella cheese on top of or around the tomatoes in the mushroom caps.
Sprinkle the mushrooms with the Parmesan cheese and drizzle with additional olive oil if desired.
Bake for about 20 minutes or until the mushrooms are softened and the cheese is melted. If desired, move the pan to the broiler for about 30 seconds at the end to brown the cheese a bit.
Sprinkle with the remaining fresh basil and serve.