01 - In a large pot set over medium heat, melt the unsalted butter. Add the finely diced onion, carrot, and minced garlic. Sauté gently for approximately 5 minutes, or until the vegetables are softened and aromatic.
02 - Stir in the tomato paste and cook for 1 minute, allowing it to deepen in color and flavor. Incorporate the undrained diced tomatoes, vegetable broth, granulated sugar, salt, black pepper, dried oregano, and the bay leaf. Bring the mixture to a gentle simmer.
03 - Reduce the heat to low, cover the pot, and allow the bisque to simmer for 20 minutes, stirring occasionally to prevent sticking.
04 - Carefully remove and discard the bay leaf. Add the fresh basil leaves to the soup.
05 - Using an immersion blender, carefully puree the soup directly in the pot until it reaches a smooth and velvety consistency. Alternatively, transfer the soup in batches to a standard blender, blending until smooth, then return to the pot.
06 - Return the pureed soup to low heat. Stir in the heavy cream and the optional grated Parmesan cheese. Heat gently for 2 to 3 minutes, ensuring the bisque does not come to a boil.
07 - Taste the bisque and adjust seasoning as necessary. Serve hot, garnished with extra fresh basil.