1. Heat oven to 425°F/220°C. Add tomatoes (cut-side up), onion, and garlic to a rimmed sheet pan. Drizzle with olive oil, salt, and pepper; roast until jammy and caramelized at edges, 25–30 minutes.

2. Scrape everything (and juices) into a pot. Add tomato paste; cook 1 minute to caramelize.

3. Pour in broth and sugar; simmer 10 minutes. Add basil and blend until silky with an immersion blender (or carefully in a blender).

4. Stir in cream if using and adjust salt/pepper. Keep warm over low heat.

5. Make grilled-cheese: butter bread, sandwich cheese, and griddle until golden. Cool 2 minutes, then cut into bite-size croutons.

6. Ladle soup into bowls and top with grilled-cheese croutons and extra basil.