Heat the butter and garlic in a skillet over medium heat until the butter begins to bubble. Stir in the shrimp, and cook until they just turn pink, about 3 minutes. Place one shrimp into each mushroom cap, and place into a small baking dish. Spoon the garlic butter into the mushroom caps, and sprinkle each with a pinch of mozzarella cheese.
Bake in the preheated oven until the mushrooms are tender and the cheese is golden and bubbly, 10 to 15 minutes.
