01 - Preheat oven to 425°F. Arrange red bell peppers on a baking sheet and roast for 20 to 25 minutes, turning occasionally, until skins are blackened and blistered.
02 - Transfer hot peppers into a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel off charred skins, remove seeds, and roughly chop the flesh.
03 - Heat olive oil in a large pot over medium heat. Add onion and carrot; sauté for 5 to 6 minutes until soft. Add garlic and cook for 1 minute.
04 - Stir in chopped roasted peppers, canned tomatoes, smoked paprika, and sugar. Season with salt and pepper. Cook for 5 minutes, stirring occasionally.
05 - Pour in vegetable broth and bring to a boil. Reduce heat to low and simmer uncovered for 15 minutes.
06 - Remove pot from heat. Add fresh basil leaves and blend the soup until completely smooth using an immersion blender.
07 - Stir heavy cream into the soup. Taste and adjust salt and pepper if necessary.
08 - Ladle soup into bowls and garnish with extra basil leaves before serving hot.