Cut each avocado in half lengthwise and remove the pit. Use a spoon to scoop out some of the flesh gently, creating a larger cavity for stuffing. Save the scooped avocado for another use or mash it for a dip.
In a mixing bowl, combine the halved cherry tomatoes, mozzarella, and torn basil. Drizzle with olive oil, season with salt and pepper, and toss gently to coat the ingredients evenly.
Spoon the tomato-mozzarella mixture into the avocado halves, filling them generously.
Drizzle the balsamic glaze over the stuffed avocados for an added flavor kick.
Serve immediately as a refreshing appetizer or a light meal.