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 20 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 regular blender.
Return the pureed soup to the pot and stir in the heavy cream. Heat over low until warmed through, about 5 minutes.
Serve hot, garnished with fresh basil leaves.