In a large pot, heat 2 tablespoons of olive oil over medium heat. Add 1 chopped onion, stirring frequently, and cook for 5-7 minutes until it becomes translucent and fragrant. Then, add 3 minced garlic cloves and sauté for an additional minute.

Stir in 2 cans of crushed tomatoes and 3 cups of vegetable broth. Sprinkle in 1 teaspoon of dried basil, a pinch of sugar, and season with salt and black pepper to taste. Increase the heat until it comes to a gentle boil, then reduce the heat and let it simmer uncovered for 15-20 minutes.

Remove the pot from the heat. Using an immersion blender, blend the soup until it reaches a silky smooth consistency, or transfer it to a regular blender in batches. Return the pureed soup to the pot.

With the soup back on low heat, gradually stir in 1 cup of heavy cream until fully incorporated. Allow it to warm through for another 3-5 minutes.

Ladle the warm soup into bowls, garnishing with fresh basil if desired. Pair it with crusty bread or a classic grilled cheese sandwich.