Prepare and Roast Vegetables: Preheat oven to 400°F and line a baking sheet with parchment paper. Arrange tomatoes (cut side up), onion wedges, and peeled garlic cloves on the baking sheet. Drizzle everything with olive oil and sprinkle with salt, pepper, and sugar. Roast for 45 minutes until all vegetables are completely softened. Once slightly cooled, peel the tomatoes to remove the skins.

Make Grilled Cheese: While vegetables are roasting, prepare the grilled cheese sandwiches. Butter one side of each bread slice. Place a slice in a non-stick skillet over low heat (buttered side down), top with a slice of cheddar cheese and another bread slice (buttered side up). Cook about 3 minutes per side until golden brown with melted cheese. Repeat for second sandwich. Cut each sandwich into approximately ½-inch cubes (about 16 pieces each) and set aside.

Blend the Soup: Add peeled roasted tomatoes and other roasted vegetables to a large pot with chicken broth and chopped basil. Use an immersion blender to puree until smooth, then set over medium heat.

Finish the Soup: Add heavy cream, grated parmesan, and garlic salt to the soup. Cook while stirring occasionally until thoroughly warmed and cheese has completely melted into the soup.

Prepare for Broiling: Move oven rack to the top-middle position and set to broil. Place five oven-safe bowls (6 oz each) on a baking sheet and divide soup evenly among them. Top each bowl with 6-7 grilled cheese croutons, followed by ¼ cup Gruyere cheese and ¼ cup sharp cheddar cheese.

Broil and Serve: Place the soup bowls under the broiler for 2-3 minutes, watching carefully, until cheese bubbles and begins to brown. Allow to cool slightly before serving, garnish with fresh chopped basil if desired.