Preheat the oven to 275°F (135°C).
In a medium oven-safe dish, combine the halved cherry tomatoes, 2 tablespoons olive oil, minced garlic, fresh thyme leaves, sugar, salt, and black pepper. Stir to coat the tomatoes evenly.
Place the dish in the preheated oven and roast the tomatoes slowly for 1 hour, stirring halfway through, until the tomatoes are soft and flavorful but still hold their shape. Remove from the oven and let cool slightly.
While the tomatoes roast, lightly toast the ciabatta rolls in a toaster or oven until golden and crisp.
Once the tomato confit has cooled slightly, spread a spoonful generously over the bottom half of each toasted ciabatta roll.
Tear the burrata cheese into large pieces and layer evenly over the tomato confit on each sandwich.
Distribute fresh basil leaves evenly on top of the burrata.
Drizzle 1/2 tablespoon of olive oil and 1/2 tablespoon of balsamic glaze over the basil on each sandwich.
Place the top half of the ciabatta roll on each sandwich and press down gently.
Serve immediately and enjoy the rich, fresh flavors.