Does anybody know exactly how to make ARBY's potato cakes?

That isn’t even remotely like Arby’s, devilsknew. Giiod, maybe, but not Arby’s.
When you bite into an Arby’s, it’s like the whole thing is made of shredded potato. Of course it isn’t - it has to have a binder, probably flour and egg. But I don’t remember Arby’s having ANY special seasoning. Just deep fried potato.

A favorite potato of mind is Potatoes Ana. The spud has to be sliced paper-thin, then tossed in melted butter to coat and spread out evenly in a baking pan, and baked till golden. It’s best to bake it in one layer, two at the most, but if you use more, it’s okay, but the middle slices won’t get crispy. They’ll be sort of creamy, but that’s not bad.
They’re like french fries with a college education - fried in butter, and thin crispy slices. All you need with it is S&P.

A somewhat less fattening version would be *gratin Savoyard *.

Shave a big peeled yukon gold potato thin on the mandoline side of your box grater, lay half of it evenly over a buttered baking dish. Cover with salt, pepper, and a half cup of shredded Gruyere or another Swiss-style cheese. Put the rest of the potatoes over, pour in 3/4 cup beef or chicken stock, more S&P, then cover and bake at 375 for 40 minutes. Uncover and bake another ten minutes, until top crisps.