Melt the butter in a large, heavy-bottomed pot or Dutch oven over medium heat. Add the finely diced onion, celery, and carrot. Cook, stirring occasionally, until the vegetables are softened and translucent, about 5-7 minutes.

Stir in the minced garlic and cook for an additional minute until fragrant. Sprinkle the all-purpose flour over the vegetables and stir constantly for one minute, creating a roux that will thicken the bisque.

Gradually whisk in the chicken or vegetable broth, ensuring no lumps remain. Add the undrained fire-roasted diced tomatoes, granulated sugar, tomato paste, dried basil, and a pinch of ground nutmeg. Bring the mixture to a gentle boil, then reduce the heat to low, cover, and simmer for 15 minutes to allow the flavors to meld.

Carefully remove the pot from the heat. Use an immersion blender to purée the soup directly in the pot until it is completely smooth and creamy. Alternatively, you can transfer the soup in batches to a standard blender, blending until silky, then return it to the pot.

Stir in the heavy cream and return the pot to medium-low heat. Cook, stirring gently, until the bisque is heated through. Avoid bringing the soup to a rolling boil after adding the cream to prevent curdling.

Season the creamy tomato bisque generously with fine sea salt and freshly ground black pepper to taste. Ladle into bowls and serve immediately, garnished with fresh basil, a drizzle of olive oil, or grated Parmesan cheese if desired.