How to Make It
Preheat the oven to 400°. Spread a layer of kosher salt 1/2 inch thick in a large, deep roasting pan. Nestle the potatoes in the salt and cover with the remaining salt. Bake in the center of the oven for about 1 1/4 hours, or until the potatoes are tender.
Meanwhile, in a small saucepan of boiling water cook the dark green scallion until softened and bright green, about 20 seconds. Drain and rinse the scallion greens in cold water, transfer to a mini food processor and finely chop. Add 1 stick of the butter and pulse until combined. Add the white and light green sliced scallion and a pinch each of table salt and pepper and pulse until incorporated. Scrape the butter into a ramekin and refrigerate until firm or keep at room temperature.
Wipe out the food processor. Add another stick of butter, the grainy mustard, Dijon mustard and a pinch each of salt and pepper. Pulse just until blended. Scrape the butter into a ramekin and refrigerate until firm or keep at room temperature. Repeat with the remaining stick of butter, the horseradish, lemon juice and a pinch each of salt and pepper.
When the potatoes are done, carefully brush off the salt and transfer them to a platter. Serve the potatoes with the flavored butters.