Preheat the oven to 375°F (190°C).
Clean the Portobello mushrooms and carefully remove the stems.
In a skillet, melt the butter over medium heat, then add minced garlic.
Add halved cherry tomatoes to the skillet and cook until they soften, about 3-4 minutes.
Stir in the diced mozzarella and chopped basil, seasoning with salt and pepper.
Fill each Portobello cap with the tomato and mozzarella mixture.
Place the stuffed mushrooms on a baking sheet and drizzle with extra melted garlic butter.
Bake for 20-25 minutes, until the mushrooms are tender and the cheese is bubbly.
Remove from the oven, drizzle with balsamic glaze, and serve warm.