Heat olive oil or butter in a medium-sized pot over medium heat.
Add the chopped onion and sauté until softened, about 5 minutes.
Stir in the garlic and cook for 1 minute until fragrant.
Add the crushed tomatoes, vegetable broth, dried basil, and sugar (if using). Stir to combine.
Bring the soup to a gentle simmer and cook for 10–15 minutes, allowing the flavors to meld.
Remove from heat and blend the soup using an immersion blender until smooth (or carefully transfer to a blender in batches).
Stir in the heavy cream or coconut milk.
Season with salt and pepper to taste.
Serve warm, garnished with fresh basil leaves.
Pair with crusty bread or grilled cheese for extra comfort!