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