In a large casserole pot, heat oil over medium-high heat.
Add onion, garlic, celery and carrot and saute until all vegetables are soft, about 6 minutes.
While the vegetables are cooking, pour the tomatoes into a bowl and crush with your hands. Discard any hard cores or yellow portions.
Add the hand crushed tomatoes to the vegetable mixture, then tear the basil leaves into the sauce.
Bring to a low boil then reduce the heat to low. Cover the pot and simmer for 1 hour or until thick.
Taste for seasoning, add salt and pepper to your taste.
If sauce is too acidic, add unsalted butter, 1 Tablespoon at a time, to round out the flavor.
Using an immersion blender, blend the tomato sauce until smooth. (To blend the sauce, a food processor or blender can also be used blending only ½ of the sauce at a time.)