Heat the vegetable oil in a Dutch oven over medium heat. Add the onion and celery and cook until softened, about 5 minutes.
Stir in the garlic and cook until fragrant, about 30 seconds. Sprinkle in the flour and cook for 1 minute, stirring constantly. Add the tomatoes and chicken broth.
Bring the soup to a boil. Reduce the heat, cover, and simmer for 15 minutes. Use an immersion blender to blend the soup until smooth. Alternatively, carefully transfer the soup to a blender and puree until smooth.
Reduce the heat to low and stir in the butter and heavy cream until melted and fully incorporated. Add the dried basil, sugar, garlic powder, onion powder, and cayenne pepper, if using. Season with salt and black pepper to taste, stirring until the bisque is smooth, creamy, and a beautiful light orange color.
To make the cheesy bread, place slices of French or ciabatta bread on a baking sheet and top with shredded cheese.
Ladle the tomato bisque into bowls and top with cheesy bread or croutons.