01 - Set the oven to 400°F and line a baking sheet with parchment paper.
02 - Place halved tomatoes cut side up, chopped onion, carrot, and whole garlic head on the baking sheet. Drizzle with olive oil, then season with salt and black pepper.
03 - Roast in the oven for 35 to 40 minutes, until the tomatoes blister and the garlic softens and turns golden.
04 - Allow the garlic to cool briefly, then squeeze the softened cloves from the bulb.
05 - Transfer the roasted tomatoes, onion, carrot, and extracted garlic into a large pot. Add the vegetable broth, fresh basil leaves, dried oregano, and crushed red pepper flakes if using.
06 - Bring the mixture to a simmer and cook gently for 10 minutes to develop the flavors.
07 - Blend the simmered vegetables until smooth using an immersion blender or in batches with a countertop blender.
08 - Taste and season with additional salt and pepper as desired.
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 immediately while hot.