Melt butter in a large pot over medium; cook onion about 5 minutes until soft and translucent.
Add garlic; cook another minute until fragrant.
Stir in tomatoes, broth, and sugar; simmer 15 minutes.
Puree with an immersion blender or carefully transfer to a regular blender in batches.
Stir in cream; season with salt and pepper and heat through without boiling.
Meanwhile, cook grilled cheese sandwiches on a griddle or skillet until both sides are golden brown.
Serve soup hot with grilled cheese for dipping.