In a saucepan over medium heat, add a splash of olive oil and sauté the chopped onion until translucent, about 5 minutes.

Add the minced garlic and cook for an additional minute until fragrant.

Stir in the crushed tomatoes, vegetable broth, salt, pepper, and sugar. Bring to a simmer and cook for 20 minutes.

Remove the saucepan from heat and add the fresh basil leaves. Use an immersion blender to puree the soup until smooth, or transfer to a blender in batches.

Return the blended soup to the saucepan and stir in the heavy cream. Heat gently until warmed through, about 5 minutes.

Ladle the soup into bowls and garnish with additional basil leaves if desired. Serve hot.