In a large pot, heat the olive oil over medium heat. This will help to sauté the onions and garlic, releasing their flavors.

Add the chopped onion and sauté for about 5 minutes, or until the onion is translucent. Stir occasionally to prevent burning.

Add the minced garlic and sauté for an additional 1-2 minutes until fragrant. Be careful not to let the garlic brown, as it can become bitter.

Pour in the crushed tomatoes and vegetable broth. Stir well to combine all the ingredients.

Add the sugar, salt, and black pepper. The sugar will help to balance the acidity of the tomatoes.

Bring the mixture to a simmer, then reduce the heat to low. Cover the pot and let it cook for about 20 minutes, allowing the flavors to meld.

Remove the pot from heat. Carefully transfer the soup to a blender in batches, or use an immersion blender directly in the pot. Blend until smooth.

If using a blender, be cautious of the hot liquid. Allow it to cool slightly before blending, and remove the center cap of the lid to let steam escape.

Once blended, return the soup to the pot over low heat. Stir in the fresh basil leaves and heavy cream, if using. Allow to heat through for about 5 minutes.

Taste and adjust seasoning if necessary, adding more salt or pepper to your preference.

Ladle the soup into bowls and garnish with additional fresh basil leaves or a drizzle of olive oil if desired.

Serve hot with crusty bread or grilled cheese sandwiches for a complete meal.