Melt the butter in a large Dutch oven or heavy-bottomed pot over medium heat.
Add the chopped onion and sauté for 5-7 minutes until soft and translucent. Add the minced garlic and cook for 1 more minute until fragrant.
Pour in the canned tomatoes (crushing them slightly with your hands or a wooden spoon as they go in), the vegetable broth, and the sugar.
Season the pot with salt and freshly ground black pepper. Bring the mixture to a gentle boil, then reduce the heat, cover, and let it simmer for 20 minutes to allow the flavors to deepen and meld.
Remove the pot from the heat. Carefully use an immersion blender (or transfer in batches to a stand blender) to puree the soup until it is velvety smooth.
Stir in the heavy cream and the chopped fresh basil. Taste and adjust the seasoning if necessary.
Serve hot in bowls, garnished with an extra swirl of cream and a fresh basil leaf, ideally alongside a crispy, buttery grilled cheese sandwich!