Prep the tomatoes: Heat the oven to 425°F (220°C). Halve the tomatoes (leave cherry tomatoes whole), and spread them on a large sheet pan. Add the garlic cloves (leave them in their skins so they don’t burn).

Season and roast: Drizzle the tomatoes and garlic with 2–3 tablespoons of olive oil. Sprinkle with salt and pepper. Roast for 25–35 minutes, until the tomatoes are soft, blistered, and starting to caramelize around the edges.

Sauté the aromatics: While the tomatoes roast, warm 1 tablespoon olive oil (and butter if using) in a large pot over medium heat. Add the chopped onion and a pinch of salt. Cook 6–8 minutes, stirring often, until soft and lightly golden.

Build the base: Stir in tomato paste and cook for 1–2 minutes to caramelize it. Add a pinch of red pepper flakes if you like a little heat.

Add the roasted tomatoes: Squeeze the roasted garlic out of their skins into the pot. Scrape all the tomatoes and their juices from the sheet pan into the pot. Add 3 cups of broth and the Parmesan rind if you have one.

Simmer: Bring to a gentle simmer and cook for 10–15 minutes to let the flavors meld. If it gets too thick, add more broth.

Blend: Remove the Parmesan rind. Add the fresh basil. Use an immersion blender to blend until smooth, or carefully transfer to a blender in batches. For a very silky texture, blend longer than you think you need.

Finish: Stir in cream or coconut milk if using. Taste and adjust with salt, pepper, and 1–2 teaspoons balsamic vinegar for brightness. If your tomatoes were very acidic, add 1/2 teaspoon sugar or honey to balance.

Serve: Ladle into bowls and garnish with torn basil, a drizzle of olive oil, and cracked pepper. Add a grilled cheese on the side if you want the classic combo.