Melt the butter in a large pot over medium heat.
Add the chopped onion, celery, and carrots.
Sauté until the vegetables are tender, about 5 minutes.
Stir in the minced garlic and flour.
Cook for about 1 minute, stirring constantly, to form a roux.
Add the tomatoes, chicken broth, sugar, salt, black pepper, and cayenne pepper.
Bring the mixture to a simmer, stirring occasionally.
Reduce the heat and let it simmer for 30 minutes.
Use an immersion blender or transfer to a blender and puree until smooth.
Return the bisque to the pot and stir in the heavy cream and chopped basil.
Heat until just warmed through.
Serve hot, garnished with more basil if desired.