A very informative video from The Pasta Channel, this fairly lengthy video (16:42) demonstrates two different methods for making an authentic Italian tomato sauce (basic) using canned San Marzano tomatoes. She goes into great detail on why San Marzano tomatoes are best and what to look for to make sure you're getting an authentic product.
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For the first sauce, which is more time consuming, the host explains how the battuto (the chopped pieces), your choice of minced vegetables and herbs...celery, carrots, garlic, onions, etc. becomes the soffritto (fried), when they are sautéed in olive oil until they become soft and caramelized, imparting the flavors to any ingredient that follows. In this sauce, the tomatoes are put through a food mill by hand first, then simmered to make a rich, thick, sauce. The longer cooking time helps sweeten the sauce.
The second sauce is a super fast sauce in which she uses large pieces of garlic and onions to flavor the oil and sauce (removing them before mixing) and cooks the tomatoes only as long as it takes to cook the pasta. A handful of fresh herbs, a drizzle of extra-virgin olive oil and a quick toss in the hot pan and it's done!