Preheat your oven to 450°F (230°C). Place the whole red bell peppers on a baking sheet lined with foil or parchment paper. Roast for about 25-30 minutes, turning every 10 minutes, until the skins are charred and blistered all over.
Transfer the roasted peppers to a bowl and cover with plastic wrap or a plate to steam for 10 minutes. Remove the charred skins, seeds, and stems, then roughly chop the peppers.
In a large pot or Dutch oven, heat olive oil over medium heat. Add diced onion and sauté until soft and translucent, about 5-7 minutes. Stir in minced garlic and cook for another 1-2 minutes until fragrant.
Add the chopped roasted red peppers, vegetable broth, dried basil, and dried oregano to the pot. Bring to a gentle boil, then reduce heat and simmer for 15-20 minutes.
Remove the pot from heat. Use an immersion blender to puree the soup until smooth and creamy. Alternatively, blend in batches in a countertop blender and return to the pot.
Pour in the heavy cream and stir to combine. Warm the soup gently over low heat. Season with salt and pepper to taste, avoiding boiling after adding cream.
Ladle the soup into bowls and garnish with fresh basil leaves. Serve warm with crusty bread or a salad.