In a large bowl, mix ground beef with garlic and basil until incorporated. Shape the beef mixture into 6 to 8 patties, or to desired size. To an oven-safe sauté pan, add the cherry tomatoes, brown sugar, balsamic vinegar, and a pinch of salt and pepper. Roast in an oven at 350°F for 20 to 30 minutes, or until the tomatoes blister and the mixture thickens to resemble jam. Season patties with salt and freshly-cracked pepper and grill to desired doneness. Top each patty with tomato jam and slices of mozzarella and serve on a bun.