Roast the Tomatoes and Garlic:

1. Preheat the Oven: Preheat your oven to 400°F (200°C).
2. Prepare the Vegetables: Place the halved tomatoes cut side up on a baking sheet. Slice off the top of the garlic head to expose the cloves and wrap it in aluminum foil.
3. Drizzle with Olive Oil: Drizzle the tomatoes with 1 tablespoon of olive oil, and sprinkle with a pinch of salt and pepper. Place the foil-wrapped garlic on the baking sheet alongside the tomatoes.
4. Roast: Roast in the oven for 30-35 minutes until the tomatoes are soft and slightly caramelized, and the garlic is golden and tender.

Prepare the Soup Base:

5. Sauté the Vegetables: Heat the remaining olive oil in a large pot over medium heat. Add the chopped onion and carrot, sautéing until softened, about 5-7 minutes.
6. Add the Roasted Ingredients: Squeeze the roasted garlic cloves out of their skins and add them to the pot along with the roasted tomatoes and their juices.

Simmer the Soup:

7. Add Broth and Seasonings: Pour in the vegetable broth, smoked paprika, and dried basil. Stir to combine.
8. Simmer: Bring the mixture to a boil, then reduce the heat and simmer for 15 minutes to blend the flavors.

Blend and Finish:

9. Blend the Soup: Use an immersion blender to puree the soup until smooth, or transfer it to a blender in batches.
10. Add Cream: Stir in the heavy cream, taste, and adjust the seasoning with salt and pepper as needed.