In a large pot, heat the olive oil over medium heat. Add the diced onion, garlic, carrot, and celery. Sauté for about 5-7 minutes until the vegetables are softened.
Stir in the crushed tomatoes, vegetable broth, dried basil, dried oregano, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 20-25 minutes, stirring occasionally.
If you prefer a sweeter soup, add the sugar and stir to combine.
For a creamy version, stir in the heavy cream and heat through for an additional 5 minutes.
Remove the pot from heat and stir in the fresh basil leaves.
Use an immersion blender to puree the soup to your desired consistency, or carefully transfer it to a blender in batches.
Taste and adjust seasoning if necessary before serving.