In a large, heavy saucepan, melt 2 tablespoons of butter and pour olive oil. Add minced garlic, fresh thyme, onions, and celery.
Cook over moderately high heat, stirring occasionally for about 5 minutes until vegetables are soft and beginning to get brown.
Sprinkle flour over the vegetables and frequently stir over low heat for about a minute until the mixture is smooth and the flour is fully incorporated. This helps to thicken the soup later.
Add tomatoes, chicken broth, and brown sugar. Season the soup with Italian seasoning, salt, and black pepper to taste.
Cover partially and cook the soup over moderate heat, stirring occasionally for about 15 minutes, until vegetables are tender. Make sure to scoop the bottom of the pan every 5 minutes to avoid burning.
Allow the soup to cool off slightly, then transfer the soup to a blender in batches and blend on high until smooth and silky. Return the puree to the saucepan.
Add the heavy cream and cook until the soup is just heated through. Ladle the soup into bowls, garnish with basil or parsley and serve with croutons. Bisque is best served warm or hot.