Preheat the oven to 350 degrees F.
In a medium bowl, and using an electric mixer, beat the egg whites until they form stiff peaks, about 2-3 minutes. Next, fold in the kosher salt.
In a 13 x 9 casserole dish (or one that's similar in size--these things don't have to be totally exact), spoon a few tablespoons of the egg white mixture to the bottom of the dish. Using the back of the spoon, create one even layer and arrange the potatoes atop. Add the rest of the egg white mixture to the top of the potatoes, smoothing it out evenly. Transfer the potatoes to the oven and bake for 40-45 minutes. Note: If you're using larger potatoes like, say, russets, increase the bake time to 1 hour. If the salt crust starts to get too brown, tent it with a piece of foil.
Meanwhile, let's make the sauce. To a small bowl, mix together the mayonnaise, minced shallot, Dijon mustard, fresh dill and ground pepper. Set aside.
Remove the potatoes from the oven and using the back of a knife, crack the formed crust. Allow to cool for 5-7 minutes before handling. Remove the potatoes and dust off the salt, thoroughly. Cube up the potatoes and transfer them to a bowl. Toss with the dressing and serve warm, or alternatively, you could cover the bowl with plastic wrap and place it in the refrigerator to cool, about 2-3 hours.