This is my family's favorite. I make it for New Year's or Christmas dinners. We adore this and love the left-overs as well. The horseradish sauce is easy and tasty. This recipe is a really do-able way to be a kitchen hero.
Sprinkle roast with 1 tablespoon salt, cover with plastic wrap, and let stand at room temperature 1 hour or refrigerate for up to 24 hours. Adjust oven rack to middle position and heat oven to 400 degrees.
Toss bread crumbs with 2 teaspoons oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper in 10-inch nonstick skillet. Cook over medium heat, stirring frequently, until deep golden brown, 3 to 5 minutes. Transfer to rimmed baking sheet and cool to room temperature (wipe out skillet). Once cool, toss bread crumbs with shallot, garlic, 2 tablespoons horseradish, parsley, and thyme.
Rinse grated potato under cold water, then squeeze dry in kitchen towel. Transfer potatoes and remaining cup oil to 10-inch nonstick skillet. Cook over high heat, stirring frequently, until potatoes are golden brown and crisp, 6 to 8 minutes. Using slotted spoon, transfer potatoes to paper towel-lined plate and season lightly with salt; let cool for 5 minutes. Reserve 1 tablespoon oil from skillet and discard remainder. Once potatoes are cool, transfer to quart-size zipper-lock bag and crush until coarsely ground. Transfer potatoes to baking sheet with bread-crumb mixture and toss to combine.
Pat exterior of tenderloin dry with paper towels and sprinkle evenly with remaining teaspoon pepper. Heat reserved tablespoon oil in 12-inch nonstick skillet over medium-high heat until just smoking. Sear tenderloin until well browned on all sides, 5 to 7 minutes. Transfer to wire rack set in rimmed baking sheet and let rest 10 minutes.
Combine remaining 2 tablespoons horseradish, mayonnaise, and mustard in small bowl. Just before coating tenderloin, add gelatin and stir to combine. Spread horseradish paste on top and sides of meat, leaving bottom and ends bare. Roll coated sides of tenderloin in bread-crumb mixture, pressing gently so crumbs adhere in even layer that just covers horseradish paste; pat off any excess.
Return tenderloin to wire rack. Roast until instant-read thermometer inserted into center of roast registers 120 to 125 degrees for medium-rare, 25 to 30 minutes.
Transfer roast to carving board and let rest 20 minutes. Carefully cut meat crosswise into 1/2-inch-thick slices and serve.
Horseradish cream sauce: Whisk cream in medium bowl until thickened but not yet holding soft peaks, 1 to 2 minutes. Gently fold in horseradish, salt, and pepper. Transfer to serving bowl and refrigerate at least 30 minutes or up to 1 hour before serving.