r540/r567 The chipped(meaning sliced so thinly as to be ALMOST shredded) beef you buy is actually cuts of meat, seasoned and preserved( with the usual suspects, plenty of salt and some sort of nitrites and nitrates, in order to retain color and keep nasty bacteria from getting a foothold) then air dried(similar to how prosciutto is made) meaning this stuff is not cooked until YOU cook it. It always has a sort of liver-ish red/dark pink color.
BITD you could buy the air-dried beef at deli counters in my area(Philly and environs always had a taste for chipped beef, what with the Amish influence and all the guys who "fondly" remembered it from being in the military), it was THAT much of a popular item(hasn't been available that way in a long time though) I haven't looked lately but a few companies used to sell it, packaged in small glass jars, usually about 3 or 4 oz. you don't need much at a time because the white sauce you make is the bulk of what you're cooking. If you're running a diner, luncheonette or any place that serves breakfast in my area you have to have SOS on there menu. Many people expect it, even if they don't always order it. I'm guessing SOS is known country-wide since it is in Stouffer's frozen line-up.
The chipped meat you buy today is invariably in plastic pouches, and not as salty as it used to be. The stuff in the old glass jars had so much salt in it that you had to rinse it under hot running water just to get the salt content down to edible levels.
If you're going to make SOS the traditional way was to sauté(or frizzle, as it used to be termed. IIRC Horn & Hardart listed what amounted to SOS as "Frizzled Beef" on their menu) the shredded beef(it was sometimes cut into strips) in butter before making the white sauce right in the same skillet. You'd cook it for a few minutes, getting it just a tad curled at the edges, you really didn't want to brown it. Next you sprinkled on flour, cooked it for a minute or so, because you were going to make a roux. Then you added the milk, stirred thoroughly, brought it to a boil and simmered it until it was at your desired density. Traditionally it was served over white toast(this was the shingle part) usually heavily black-peppered(no other spices were used)
I'm not sure why this stuff was called SHIT on a shingle, maybe the GI's just got tired of it? My best guess is it was named when the dish used to be made with ground FRESH beef, which is definitely a thing, although I've never seen it on a breakfast menu. I remember it fondly from when I was in the service, it is far more unctuous, tasty and GREASY than the chipped beef kind.
Serve it over anything you like: toast, biscuits, hash browns or home fries with onions(Mmmm....) even mashed potatoes.
My mom used to make SOS as part of a big Sunday breakfast once we all got home from church. She was a Philly gal, and my dad had been in the Navy, so she was quite aware of this Lucullan breakfast fare.