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 charred and blistered.
02 - Transfer hot peppers to a bowl, cover with plastic wrap and let steam for 10 minutes. Peel off skins, remove seeds, and roughly chop the flesh.
03 - In a large pot, heat olive oil over medium heat. Add chopped onion and diced carrot; sauté for 5–6 minutes until softened. Add minced garlic and cook for 1 more minute.
04 - Add roasted red peppers, drained canned tomatoes, smoked paprika, and sugar to the pot. Season with salt and black pepper. Cook for 5 minutes, stirring occasionally.
05 - Pour in vegetable broth and bring to a boil. Reduce heat and simmer uncovered for 15 minutes.
06 - Remove pot from heat. Add fresh basil leaves, then puree soup until smooth using an immersion blender or by working in batches in a regular blender.
07 - Stir in heavy cream. Adjust seasoning to taste.
08 - Ladle soup into bowls, garnish with additional basil leaves, and serve warm.