Melt the unsalted butter in a large pot or Dutch oven over medium heat. Add the finely chopped onion and cook for 5 to 7 minutes, stirring occasionally, until the onion becomes soft and translucent.
Add the minced garlic to the pot and cook for 1 minute, stirring constantly, until the garlic is fragrant.
Pour in the crushed tomatoes and vegetable broth, then stir in the granulated sugar, salt, and pepper. Bring the mixture to a gentle boil, then reduce the heat to low and let it simmer uncovered for 15 minutes to allow the flavors to meld.
Carefully transfer the soup in batches to a blender, or use an immersion blender directly in the pot, and puree until the soup is completely smooth and creamy.
Stir in the heavy cream and chopped fresh basil until fully incorporated and heated through, about 2 minutes. Taste and adjust seasoning with more salt and pepper if desired.
