That Sunday special that Italian-Americans call either sauce or gravy is properly called ragú. Every nonna in Naples has her own recipe which are all variations on essentially the same thing: slow simmered meat smothered smothered in pureed tomatoes. An authentic ragù is time consuming because it must cook slowly over a whisper of a flame, but the recipe is very easy.
Here is everything you need for a Sunday ragù as good as anything you would be served in Naples.
1/4 cup extra virgin olive oil
4 garlic cloves
1 medium bone-in pork shoulder with fat
Two 28-oz. cans San Marzano tomatoes, crushed with you hands
1 tube of tomato paste
1 tablespoon Turkish oregano or wild Calabrian oregano (Most oregano in American grocery stores is Mexican and lacks the flavor of Mediterranean oregano.) Method
Cover the bottom of a large pot or dutch oven with a quarter of an inch of the olive oil. Peel the garlic and smash it with the side of your knife. Add to the oil and place the pot over a very low flame. Use a wooden spoon to move the garlic through the oil to season it as it becomes soft and translucent (about five minutes) and then remove and discard.
Raise the flame to medium and add your pork shoulder. Let it brown, about 3-4 minutes on each side.
Add the crushed tomatoes right over the pork shoulder and stir with a wooden spoon to combine the tomatoes with the oil and fat from the pork. Stir slowly and add the oregano. Once warm add the entire tube of tomato paste and stir to combine once again.
Cover the pot and turn the flame down to the lowest possible whisper. Let it cook for 3-4 hours, stirring occasionally.
Return to the pot and use a spoon to remove the ribbons of fat oil that have risen to the top. Stir once again letting the chunks of meat fall into the sauce. Serve over pasta or with a "scarpetta", a hunk of bread nicknamed "little shoe" in Italian.