Preheat the oven to 375 degrees F. Scrub the beets; remove the greens and reserve for another use. Layer 1 cup of the kosher salt in a small baking dish. Place the beets on the salt and cover the dish tightly with foil. Bake until fork-tender, about 1 hour. Remove the beets from the oven, let cool, peel with paper towels or a clean kitchen towel and shred on the coarse holes of a box grater. Transfer to a bowl.
Process the chopped horseradish and the remaining 1 tablespoon salt in a food processor until granulated, then add the white vinegar, apple cider vinegar and the sugar until smooth. Add this mixture to the beets, cover and marinate overnight in the refrigerator.
The next day, drain the beets in a colander set over a bowl. Reserve the horseradish-beet vinegar to pickle turnips or use in vinaigrette. Toss the marinated beets with Dijon mustard, olive oil, shallots, chopped fresh dill and parsley and a pinch of salt. Scatter some grated horseradish, a couple of sprigs of dill and some fresh parsley leaves on top, then finish with a drizzle of olive oil.
Be sure that the white vinegar is certified kosher for Passover as some are made from wheat.
Dijon mustard is kitniyot and is not consumed in Ashkenazi communities during Passover.