01 - Preheat the oven to 400°F and line a baking sheet with parchment paper.
02 - Arrange halved tomatoes cut side up, chopped onion, chopped carrot, and whole garlic head on the baking sheet. Drizzle with olive oil and season with salt and pepper.
03 - Roast the vegetables for 35 to 40 minutes until the tomatoes are blistered and the garlic is soft and golden.
04 - Allow the garlic to cool slightly, then squeeze the softened cloves from the bulb.
05 - Transfer the roasted vegetables and garlic to a large pot. Add vegetable broth, fresh basil, dried oregano, and crushed red pepper flakes if using.
06 - Bring to a simmer and cook for 10 minutes to meld the flavors.
07 - Use an immersion blender to puree the soup until smooth, or carefully blend in batches using a countertop blender.
08 - Taste and adjust seasoning with additional salt and black pepper as needed.
09 - Stir in heavy cream if desired for a richer texture.
10 - Ladle the soup into bowls, garnish with extra basil leaves, and serve hot.