01 - Preheat oven to 425°F. Place red bell peppers on a baking tray and roast for 20–25 minutes, turning occasionally, until skins are blistered and charred.
02 - Transfer hot peppers to a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel skins, remove seeds, and roughly chop flesh.
03 - Heat olive oil in a large pot over medium heat. Add chopped onion and diced carrot, sauté for 5–6 minutes until softened. Add minced garlic and cook for 1 additional minute.
04 - Add roasted peppers, drained tomatoes, smoked paprika, sugar, salt, and pepper to pot. Cook for 5 minutes, stirring occasionally.
05 - Pour in vegetable broth. Bring to a boil, then reduce heat and simmer uncovered for 15 minutes.
06 - Remove from heat. Add fresh basil leaves. Puree soup until smooth using an immersion or regular blender in batches.
07 - Stir in heavy cream. Adjust seasoning as needed.
08 - Ladle soup into bowls, garnish with additional basil leaves, and serve hot.