1. Heat the olive oil in a large Dutch oven over medium heat. Add the chopped onion and cook for about 5 minutes, stirring often, until soft and lightly golden. Add the garlic and cook for 1 minute.

2. Pour in the crushed tomatoes and vegetable broth. Stir well and bring the mixture to a gentle simmer.

3. Simmer the soup uncovered for 15 to 20 minutes. Stir occasionally, then add the sugar, salt, and black pepper.

4. Blend the soup with an immersion blender until smooth. Keep the soup over low heat, then stir in the heavy cream and chopped basil. Cook gently for 2 to 3 minutes.

5. Spread softened butter over one side of each bread slice. Add garlic powder or chopped herbs to the butter when desired. Place cheddar and optional mozzarella between two bread slices, keeping the buttered surfaces on the outside.

6. Heat a cast-iron skillet or nonstick pan over medium heat. Cook each sandwich for 2 to 3 minutes per side until the bread turns golden and the cheese melts. Rest for 1 minute, then slice diagonally.

7. Ladle the hot tomato basil soup into bowls. Garnish with fresh basil, black pepper, cream, or Parmesan. Serve immediately with the grilled cheese sandwiches.