01 - Preheat the oven to 400°F.
02 - Arrange the tomatoes cut side up, onion, carrot, and celery on a large baking sheet. Place the head of garlic cut side up on the sheet. Drizzle all vegetables and garlic with olive oil and sprinkle with salt and pepper.
03 - Roast for 35-40 minutes, until the vegetables are soft and caramelized and the garlic is golden and fragrant.
04 - Let the garlic cool slightly, then squeeze the roasted cloves from their skins.
05 - In a large pot over medium heat, add the roasted vegetables, squeezed garlic, tomato paste, and vegetable broth. Stir to combine.
06 - Bring to a simmer and cook for 10 minutes, allowing flavors to meld.
07 - Add basil leaves and oregano if using. Use an immersion blender to purée the soup until smooth, or carefully blend in batches in a countertop blender.
08 - Taste and adjust seasoning with salt, pepper, and sugar if needed. For a creamier soup, stir in heavy cream or half-and-half.
09 - Serve hot, garnished with extra basil leaves and a drizzle of olive oil if desired.