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