Prepare the soup base: In a pot, melt butter over medium heat. Add diced onions and sauté until translucent, about 3-4 minutes. Add minced garlic and cook for another minute until fragrant.

Add tomatoes and broth: Pour in the crushed tomatoes and vegetable broth. Stir in sugar, dried basil, salt, and pepper. Bring to a simmer and let it cook for 15 minutes.

Blend the soup: Use an immersion blender to puree the soup until smooth. Alternatively, transfer to a blender in batches. Return to the pot and stir in heavy cream. Keep warm on low heat.

Make the grilled cheese: Heat a skillet over medium heat. Butter one side of each bread slice. Place one slice butter-side down, add cheese, then top with another slice butter-side up.

Cook the sandwich: Grill each sandwich for 3-4 minutes per side until golden brown and cheese is melted. Press lightly with a spatula for even browning.

Serve: Ladle the hot tomato soup into bowls. Cut the grilled cheese sandwiches diagonally and serve alongside the soup. Enjoy immediately.