01 - Set oven to 400°F.
02 - Slice the top of the garlic head to expose cloves, drizzle lightly with olive oil, then wrap in foil.
03 - Place tomatoes cut side up, onion quarters, chopped carrot, and celery on a baking sheet. Drizzle with 2 tbsp olive oil, season with salt and pepper, and add the wrapped garlic.
04 - Roast in the oven for 35 to 40 minutes until tomatoes are soft and slightly caramelized and garlic turns golden.
05 - Squeeze roasted garlic cloves out of their skins.
06 - Transfer roasted vegetables and garlic to a large pot, add vegetable broth, oregano, and sugar if desired; bring to a simmer over medium heat and cook for 10 minutes.
07 - Add basil leaves and blend until smooth using an immersion blender or regular blender in batches.
08 - Stir in heavy cream or coconut cream if using, then adjust seasoning with salt and pepper.
09 - Serve immediately, garnished with extra basil or a drizzle of olive oil.