Preheat oven to 400°F. Line a baking sheet with parchment paper.
To the lined baking sheet, add tomatoes (cut side up), onions, and garlic.
Drizzle the entire sheet with olive oil. Sprinkle with salt, pepper, and sugar.
Roast for 45 minutes, or until the vegetables have softened completely. After they have cooled a bit, peel the tomatoes.
While the tomatoes are roasting, prepare the grilled cheese sandwiches.
Butter each slice of bread on one side.
In a non-stick skillet over low heat, add one slice of bread (buttered side down). Top with 1 slice of cheese and another slice of bread (buttered side up).
Cook for about 3 minutes on each side, or until golden brown and the cheese is melted.
Remove the sandwich from the pan. Repeat steps to make the second sandwich.
Cut each grilled cheese sandwich into ½-inch cubes, or about 16 pieces each. Set aside.
After peeling the roasted tomatoes and removing any stems, add the roasted vegetables to a large pot.
Add chicken broth and basil. Blend with an immersion blender and set over medium heat.
Add the heavy cream, parmesan, and garlic salt. Cook, stirring occasionally until the soup is warmed through and the cheese has melted.
Arrange the oven rack to the top middle position and set the oven to broil.
Place 5 small (6 ounces each) oven-safe bowls or ramekins on a large baking sheet. Divide the soup evenly into each of the 5 bowls and top each with 6-7 grilled cheese croutons, then ¼ cup of Gruyere, and then ¼ cup sharp cheddar.
Place the bowls of soup under the broiler for 2-3 minutes, or until the cheese bubbles and browns, watching carefully.
Cool slightly before serving.