In a large pot, heat the olive oil over medium heat. Add the chopped onion, garlic, carrot, and celery. Sauté for 5-7 minutes until the vegetables have softened.
Add the chopped tomatoes to the pot, along with the dried basil and sugar. Stir well, and let everything cook for another 5 minutes until the tomatoes start to break down.
Pour in the vegetable broth and bring the mixture to a boil. Once boiling, reduce the heat to low and simmer for 15 minutes, allowing the flavors to meld.
Using an immersion blender, carefully blend the soup until it's smooth and creamy. If you don't have an immersion blender, transfer the soup in batches to a countertop blender, then return it to the pot.
Stir in the coconut milk and season with salt and pepper to taste. Let the soup simmer for an additional 5 minutes to warm through.
Remove from heat and serve hot, garnished with fresh basil leaves.