01 - Preheat the oven to 425°F. Place the red bell peppers on a baking tray and roast for 20 to 25 minutes, turning occasionally, until the skins are charred and blistered.
02 - Transfer the roasted peppers to a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel off the skins, remove seeds, and roughly chop the flesh.
03 - In a large pot, heat olive oil over medium heat. Add the chopped onion and diced carrot, sautéing for 5 to 6 minutes until softened. Add minced garlic and cook for an additional minute.
04 - Add roasted red peppers, drained canned tomatoes, smoked paprika, sugar, salt, and pepper to the pot. Cook for 5 minutes, stirring occasionally.
05 - Pour in the vegetable broth and bring to a boil. Reduce heat and simmer uncovered for 15 minutes.
06 - Remove from heat and add fresh basil leaves. Using an immersion blender, purée the soup until smooth, or transfer in batches to a regular blender.
07 - Stir in the heavy cream, adjust seasoning to taste, and mix well.
08 - Ladle the soup into bowls, garnish with additional basil leaves, and serve hot.