Preheat the oven to 275°F (135°C).
In a baking dish, combine the halved cherry tomatoes, 2 tablespoons of extra virgin olive oil, granulated sugar, 1/4 teaspoon salt, and 1/8 teaspoon black pepper. Toss gently to coat evenly.
Place the baking dish in the oven and roast the tomatoes slowly for 40 minutes, until they are soft and slightly caramelized. Remove from oven and let cool slightly.
While the tomatoes roast, prepare the ciabatta rolls by slicing them horizontally and lightly toasting them if desired.
Once the tomato confit has cooled slightly, season with the remaining 1/4 teaspoon salt and 1/8 teaspoon black pepper, and stir gently.
Drizzle the remaining 1 tablespoon of olive oil on the cut sides of the ciabatta rolls.
Place half of the burrata cheese on the bottom half of each ciabatta roll, tearing it slightly for better coverage.
Spoon the tomato confit evenly over the burrata cheese on each sandwich.
Distribute 6 fresh basil leaves evenly over the tomato confit on each sandwich.
Drizzle 1 tablespoon of balsamic glaze over the basil leaves on each sandwich.
Close the sandwiches with the top halves of the ciabatta rolls and serve immediately.