Prepare the Garlic Butter: In a small saucepan over low heat, melt the butter gently. Add the crushed garlic and chopped parsley, stirring occasionally until fragrant—this usually takes about 2-3 minutes. Remove from heat and set aside.
Ready the Mushrooms: Carefully wipe the Portobello mushrooms with paper towels to absorb any moisture, which helps prevent sogginess during cooking. Place the mushrooms on a baking sheet with the bottoms facing up.
Apply Garlic Butter and Arrange Mushrooms: Using a pastry brush, generously coat the bottom (outside) of each mushroom cap with the prepared garlic butter. Then flip the mushrooms over and brush the inside cavity with any remaining garlic butter, ensuring every nook is flavored.
Fill the Mushrooms: Layer each mushroom cavity with thin slices of mozzarella, followed by an even spread of sliced grape tomatoes. The fresh cheese will melt beautifully as they cook, creating a creamy, gooey texture.
Broil to Perfection: Position the oven rack in the middle and preheat the broiler on high. Place the baking tray under the broiler and cook for about 8 minutes, or until the cheese is melted, bubbling, and just beginning to brown.
Make the Balsamic Glaze: While the mushrooms broil, pour balsamic vinegar (and brown sugar, if using) into a small saucepan over medium-high heat. Bring it to a gentle boil, then reduce the heat to low. Simmer the mixture until it thickens and reduces to a syrupy consistency, about 5-8 minutes. Keep an eye on it to prevent burning.
Final Touches and Serving: Remove the mushrooms from the oven, sprinkle fresh basil leaves on top, and drizzle with the balsamic glaze. Add a pinch of salt to taste and serve immediately for the best flavor and texture.