Add six quarts of water and one and a half cups of kosher salt to a large pot. Stir until the salt is mostly dissolved.

Add the potatoes to the brine and bring to a boil over high heat. Reduce to a steady boil and cook for 20 to 25 minutes, until the potatoes are easily pierced with a fork.

Drain the potatoes and return them to the hot pot. Let them sit for 1 to 2 minutes so the residual heat evaporates the moisture and a white salt crust forms on the skin.

Transfer the potatoes to a serving bowl and serve immediately with melted butter for dipping.