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