Sauté the Vegetables
In a large pot, heat the olive oil over medium heat. Add the diced onion, garlic, and carrot. Sauté until softened, about 5 minutes, stirring frequently to prevent browning.
Add Tomatoes and Broth
Add the chopped tomatoes (or canned tomatoes), vegetable or chicken broth, tomato paste, dried basil, and dried thyme. Stir to combine.
Simmer
Bring the mixture to a boil, then reduce the heat to low. Let it simmer for 20-25 minutes, allowing the flavors to meld and the vegetables to become tender.
Blend Until Smooth
Use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a regular blender and blend until smooth.
Add the Cream
Return the soup to low heat, then stir in the heavy cream. Season with salt and pepper to taste, and warm through without bringing it to a boil.
Serve
Ladle the bisque into bowls, garnish with fresh basil or parsley, and serve with crusty bread or a grilled cheese sandwich.