01 - Set oven to 400°F to prepare for roasting vegetables.
02 - Slice the top off the garlic head to expose cloves, drizzle with olive oil, then wrap tightly in foil.
03 - Place tomatoes cut side up, quartered onion, chopped carrot, and celery on a baking sheet. Drizzle with olive oil, season with salt and pepper, and add the wrapped garlic head.
04 - Roast for 35 to 40 minutes until tomatoes are soft and lightly caramelized and garlic turns golden brown.
05 - Squeeze the softened garlic cloves out of their skins into a bowl.
06 - Transfer roasted vegetables and garlic into a large pot, add vegetable broth, dried oregano, and sugar if using, then bring to a gentle simmer over medium heat for 10 minutes.
07 - Add fresh basil leaves and puree the mixture until smooth using an immersion blender or in batches with a standard blender.
08 - Incorporate heavy cream or coconut cream if desired, adjust seasoning with salt and pepper to taste.
09 - Ladle hot soup into bowls and garnish with extra basil leaves or a drizzle of olive oil.