Place the oil or butter in a heavy bottomed pot and heat over medium-low heat. Add the onion, garlic, tomato and celery and cook a few minutes until soft, about 5-7 minutes. Add in oregano and thyme. If using whole tomatoes, roughly chop them and toss in the pot—skins, seeds and all. If using frozen, add entire contents from packaging into the pot, and stir. Crush and mash the tomatoes with the back of your wooden spoon.
When the tomatoes have completely turned to mush, maybe 20-30 minutes, pass the mixture through a food mill. Return the sauce to the pan and reheat. Season with salt and pepper. Add chopped fresh basil.
Allow to cool slightly and store in fridge for a few days, or pour into labeled freezer-safe bags for later use.