Preheat the oven to 275°F (135°C).
In a medium bowl, combine the halved cherry tomatoes, 2 tablespoons of extra virgin olive oil, granulated sugar, 1/4 teaspoon kosher salt, 1/8 teaspoon black pepper, and minced garlic. Toss gently to coat.
Spread the tomato mixture evenly on a baking sheet lined with parchment paper.
Place the baking sheet in the oven and roast the tomatoes for 1 hour, stirring halfway through, until they are soft and slightly caramelized. Remove from oven and let cool to room temperature.
While the tomatoes roast, prepare the ciabatta rolls by slicing them horizontally and lightly toasting if desired.
Once the tomato confit has cooled, season it with the remaining 1/4 teaspoon kosher salt and 1/8 teaspoon black pepper, adjusting to taste.
To assemble each sandwich, drizzle 1/2 tablespoon of extra virgin olive oil on the cut sides of the ciabatta rolls.
Layer half of the roasted tomato confit on the bottom half of each roll.
Tear the burrata cheese into large pieces and evenly distribute over the tomatoes.
Place 4 fresh basil leaves on top of the burrata in each sandwich.
Drizzle 1 tablespoon of balsamic glaze over the basil and cheese.
Close the sandwich with the top half of the ciabatta roll and serve immediately.