In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Stir in the crushed tomatoes, vegetable broth, sugar, dried basil, salt, and black pepper. Bring the mixture to a simmer and cook for 15 minutes, stirring occasionally.
Remove the pot from heat and let it cool slightly. Use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and blend until smooth.
Return the pureed soup to the pot and stir in the heavy cream. Heat over low heat until warmed through, about 5 minutes.
Stir in the chopped fresh basil just before serving.