Preheat the oven to 400°F (200°C). Trim the tops off both garlic heads to expose the cloves. Drizzle with 1 tablespoon olive oil and wrap each head tightly in aluminum foil.

Roast for 30–35 minutes until the cloves are soft and golden. Let cool slightly.

Heat the remaining 1 tablespoon olive oil in a large pot over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté for 5–7 minutes, stirring occasionally, until softened and beginning to color.

Add the dried oregano and dried basil. Cook for 30–60 seconds until fragrant.

Squeeze the roasted garlic cloves from their skins into the pot, discarding the papery skins. Stir to combine.

Pour in the crushed tomatoes and broth. Season with salt and pepper. Increase heat and bring to a boil, then reduce to a simmer. Cook for 20 minutes to meld the flavors.

Purée the soup until smooth using an immersion blender. Alternatively, carefully transfer hot soup to a blender and blend in batches—vent the lid slightly and cover with a towel to prevent splatter.

Return the soup to low heat. Stir in the heavy cream and warm gently—do not boil after adding cream. Taste and adjust seasoning. Serve with fresh basil if desired.