In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the crushed tomatoes, vegetable broth, sugar, dried basil, salt, and black pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 15 minutes.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender and blend until smooth.
Return the soup to low heat and stir in the heavy cream. Cook for another 5 minutes, stirring occasionally.
Remove from heat and stir in the fresh basil leaves. Adjust seasoning if necessary.
Serve hot, garnished with additional basil if desired.