Preheat your oven to 450°F (230°C).
Cut the red bell peppers in half and remove the seeds and membranes. Place them cut side down on a baking sheet lined with aluminum foil. Roast the peppers in the preheated oven for about 20-25 minutes, or until the skins are charred and blistered.
Remove the peppers from the oven and place them in a bowl. Cover with plastic wrap and let them steam for about 10 minutes. This will make it easier to peel off the skins. Once the peppers are cool enough to handle, peel off the skins and set the roasted peppers aside.
In a large pot, heat 2 tablespoons of olive oil over medium heat. Add the chopped onion and cook until translucent, about 5 minutes. Add the minced garlic and cook for another 1-2 minutes until fragrant.
Add the roasted red peppers to the pot along with 4 cups of vegetable broth. Stir in 1 teaspoon of smoked paprika, 1 teaspoon of dried basil, and salt and pepper to taste. Bring the soup to a boil, then reduce the heat and let it simmer for about 15-20 minutes to allow the flavors to meld together.
Use an immersion blender to puree the soup until smooth. Alternatively, you can blend the soup in batches using a countertop blender. Stir in 1 cup of heavy cream and heat through for a few minutes.
Ladle the soup into bowls and garnish with chopped fresh basil or parsley. Serve hot with crusty bread on the side.