Preheat the oven to 450°F (230°C).

Place the halved tomatoes cut-side up on a large rimmed baking sheet with the quartered onion. Drizzle the trimmed garlic head with a little olive oil, wrap it loosely in foil and add it to the pan.

Drizzle the vegetables with the 2 tablespoons olive oil and season with salt, pepper and smoked paprika.

Roast for 30 to 40 minutes, until the tomatoes are very soft, jammy and slightly charred at the edges.

Let cool for 5 minutes. Squeeze the soft roasted garlic out of its skins.

Blend the roasted vegetables, garlic, basil and 1½ cups of the broth until completely smooth. For a very silky texture, strain through a fine-mesh sieve. (Blending safety: fill a countertop blender no more than two-thirds full, leave the lid vent open under a folded towel, and blend in batches.)

Pour into a pot over medium heat. Add the remaining broth and the red pepper flakes, and simmer for 10 minutes, stirring occasionally.

Stir in the cream or coconut milk, if using. Taste and adjust the salt, pepper and paprika.

Serve hot with fresh basil, a drizzle of olive oil or croutons.