Begin by peeling and chopping your roasted red peppers into bite-sized pieces. If roasting fresh peppers, char the skin under a broiler or open flame, then steam in a sealed bowl for 10 minutes before peeling. Chop the onion finely and mince the garlic cloves. Dice fresh tomatoes if using; canned diced tomatoes can be used directly.
Heat olive oil in a large soup pot over medium heat. Add the chopped onion and cook until translucent and fragrant, about 5 minutes. Add minced garlic and cook for an additional minute, stirring constantly to prevent burning.
Add roasted red peppers, diced tomatoes, dried basil, and oregano to the pot. Stir and cook for a few minutes to meld the flavors.
Pour in the vegetable broth, stir well, and bring the mixture to a boil. Reduce heat and simmer gently for 20-25 minutes to develop flavors.
Remove pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully blend in batches using a blender.
Return blended soup to low heat, stir in heavy cream and warm through without boiling. Season with salt and pepper to taste.
Ladle bisque into bowls, garnish with fresh basil leaves, and serve immediately with crusty bread or a light salad.