If you want to go from scratch:
Basic Tomato Puree/Sauce
3 lbs ripe Roma tomatoes
1 brown onion, medium-fine dice
2 cloves garlic, minced
1 - 2 tbs tomato paste
1 - 5 tbs sugar (to taste)
1 tsp - 1 tbs salt (to taste)
2 tbs minced basil
1/2 - 1 tsp red pepper flakes, or a few shakes of hot pepper sauce
Freshly ground black pepper, to taste
1/2 cup red wine, or 1/4 cup (inexpensive) balsamic vinegar
Peel and seed three pounds of fresh ripe Roma tomatoes, discard the peels and seeds. Reserve the flesh.
If you don't know how to peel and seed Romas: Set a pot of water on the fire to boil. When it's boiling, cut a small cross on the pointy end of each tomato, and drop the tomatoes three at a time in the pot. You can see the skin change texture after a minute, and the edges of the cross start to pull from the flesh. Remove the tomatoes from the water, reserve them, and add three more. When you've blanched nine tomatoes, take one of the cooler ones, and peel it over the sink. The peel should slip off pretty easily. Hold the peeled tomato in your fist and give it a squeeze. All the seeds will shoot into the sink. Reserve the peeled tomato in a separate bowl. Keep peeling and seeding until you've finished the first three tomatoes, then blanch three more, and so on, until all the tomatoes are done.
Chop a medium onion into fairly fine dice, and sweat it in a generous amount of good olive oil. Meanwhile mince a garlic clove. Toss that in the pan with the sweated onion. When the garlic softens (don't saute, don't brown) and it's aroma blooms, add between 1 and 2 tbs tomato paste. The less ripe the tomatoes, the more paste you'll need. Stir as the paste cooks and darkens, about 5 minutes. Note: It's important to cook tomato paste through, as it's powerful and unpleasant when still raw. The best way to cook tomato paste is like this, with very little else in the pan.
While the paste cooks, rough chop the tomato flesh. When the paste has darkened, add the tomatoes to the pan. Add 1 tsp of salt, and 1 tbs of white sugar, along with the wine or balsamic vinegar and/or the red pepper or hot sauce if using. Cook over medium heat, stirring, for about 10 minutes, and adjust the seasoning for salt, pepper and sweet, staying slightly under seasoned. Note: Black pepper will "hit" more in the palate and throat than red pepper, which will excite more on the tongue. If you make the sauce spicy with red pepper, it is said to be "angry" or "arabiata" in Itailian. Arabiata is molto bene with sea food.
Cook another 5 minutes, or until there is absolutely no more raw taste. Taste and adjust the seasoning again. Be careful with the salt, but don't be afraid of the sugar. It's a good friend to tomato. Although this sauce is a building block, it should taste good on its own. Remove from the heat and allow to cool slightly.
Puree the still warm tomatoes and their juice using a processor, blender, mill (very good), or by forcing them through a medium sieve (the other very good, but a lot of work). If you make the puree in a blender or processor, you may sieve it immediately afterwards. This is the best of both worlds. As you sieve, you'll see the color redden, the air come out, and the texture become silky. Add the chopped basil after pureeing.
This puree/sauce is extremely versatile. It may be used as is, or as the base for any number of longer cooked sauces. The recipe may be doubled, tripled, or enlarged to any size proportionately. We think it's a worthwhile to make a couple of gallons at a time, and freeze or can (we freeze).