In a large saucepot, heat a couple tablespoons of Olive Oil over medium heat. (if you are cooking any meat with the sauce, salt it and sear it now-just to brown each side- then remove it from the pan and set aside)
Add the diced onion and garlic, and sauté for a few minutes (about 2-3 minutes) until softened and fragrant.
Add a 6 oz can of tomato paste into the pot.
Fill the empty tomato paste can with water, and add the water slowly to the saucepot while stirring to combine.
Cook the tomato paste mixture for about 5-10 minutes, stirring constantly. (I usually cook it closer to 10 minutes). The original instructions from my mother-in-law was to cook it until "browned"...but to me that sounds misleading because it doesn't "brown" in the typical sense... it's more a certain roux-like texture that you want to cook it down to. You want the water to cook off quite a bit, and should be a fairly thickened texture.
Then stir in the 3 cans of the tomatoes (that have been blended fairly smooth).
Add in salt, basil, and crushed red pepper. Stir to combine.
If you are cooking any meat with the sauce, add it back it now.
Bring the sauce to a boil.
Add the lid (but slightly offset it so that there is a gap left open at the top). Then lower the temperature to very low to allow the sauce to just simmer.