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