Sauté Aromatics: Heat your large non reactive pot or Dutch oven over medium heat. Add the butter and let it melt. Add the finely chopped onions and sauté for 10-12 minutes, stirring occasionally, until they are very soft and golden in color. Add the minced garlic and sauté for another minute until fragrant.
Simmer Base: Pour in the crushed tomatoes (with their juice), chicken stock, chopped basil, sugar, and black pepper. Stir everything together to combine. Bring the soup to a boil over high heat, then reduce the heat to low, partially cover the pot with a lid, and let it simmer for 10 minutes to allow the flavors to meld.
Blend Soup (Optional): For a smooth and creamy texture, use an immersion blender to blend the soup directly in the pot until it reaches your desired consistency. Alternatively, carefully transfer the soup in batches to a countertop blender. Safety Tip: Only fill the blender one third full, remove the center cap from the lid, and cover the opening with a clean kitchen towel to let steam escape while blending. Return the blended soup to the pot. (Skip this step if you prefer a chunky soup).
Finish with Cream & Cheese: Place the pot back over medium heat. Stir in the heavy cream and freshly grated Parmesan cheese. Continue stirring until the cheese is fully melted and the soup is heated through. Bring to a gentle simmer. Taste the soup and adjust seasoning if needed, adding a pinch of salt, more pepper, or an extra teaspoon of sugar to balance the acidity.
Serve: Ladle the hot soup into bowls. Garnish generously with additional fresh Parmesan cheese and thinly sliced fresh basil. Serve immediately with your favorite grilled cheese sandwich.