I first saw a recipe for salt potatoes, a sort of Tapa, in an IKEA 365 cookbook, of all things, while shopping for a cast iron dutch oven, needed so I could make the much ballyhoo'd Bittman No Knead Bread. Which I never made, incidentally.
Anyway, they seemed simple enough, and how can one go wrong with salt, potatoes, and butter? One can't, I'll tell you what (that's said in my best Hank Hill voice).
After I first made them and posted about them on Flickr, a friend of mine from the East told me this is very common fair in New York and platters of them are sold at fairs and festivals, called Syracuse Salt Potatoes. Indeed, there is a Wiki page for it, so no further investigation is required.
Bring a pot of heavily salted water to a boil, and I do mean heavily salted. This is about a 3 quart pan and I added at least 2 cups of Kosher Salt to it. Add small red potatoes which have been scrubbed, but not pierced or cut. After this stellar shot for those who do not know what boiling water looks like, I remembered I had a small bag of Russian Fingerlings going dodgy, so I added those as well and thew in more water and salt.
Boil those pupplies at a rapid boil for about 15 minutes. Resist the urge to pierce. You don't want them breaking or absorbing too much salt.
Boiling is done. Check for tenderness. They are done when the largest potato is fork tender. You'll have to eat that one for the good of the batch. Also, when the water level drops and the tops of some of the spuds peak out, you'll notice as soon as they hit the air, they begin to turn a little white. That's good. See how as soon as I take one out of the water, it turns white? That's the fine mist of salt clinging to it. That's good.
Drain the spuds thouroughly and allow to dry. The original recipe called for baking them at a high heat for another 10 minutes to throughly dry, and I did it the first time, but not thereafter. It's a non-essential step unless you want a crispier exterior. I think they are fine as is.
Melt some butter for dipping. The sprinkled thyme is my idea (those are the little dark clumps which have already sunk to the bottom of the butter). I love thyme on just about everything and I grow it in abundance, so in it goes. Dip the hot, salty potatoes in the melted butter. Comfort food at its finest, and, no deep fat frying required. Of course you ARE eating melted butter, so it's not exactly low cal, but just few will sate you.
How salty are they? No more salty than your standard order of french fries. By not piercing the skins, only the exterior is coated in salt water, and the white film is thin, thin thin. You're not going to get salt on your hands or anything. In fact, I think a slice of bacon is saltier than these potatoes. Your pan, stove, and lid WILL be white with salt, however. It gets everywhere.