Preheat the oven to 275 degrees F. Line a sheet pan with aluminum foil.
Pat the entire tenderloin dry with paper towels and brush it all over (top and bottom) with the butter. Sprinkle the tenderloin all over with 4 teaspoons salt and 2 teaspoons pepper. It will seem like a lot but trust me, it's important.
Place the tenderloin on the prepared sheet pan and roast it for 1 to 1 1/4 hours, until an instant-read thermometer inserted into the end of the filet registers 130 degrees F for medium rare. Remove from the oven, cover tightly with aluminum foil, and allow to rest at room temperature for 15 minutes. Discard the foil and allow to sit at room temperature.
Meanwhile, for the sauce, whisk together the mayonnaise, sour cream, mustards, horseradish, and 1/4 teaspoon salt in a small bowl. Refrigerate until ready to serve.
Remove the strings and slice the filet between 1/4 and 1/2 inch thick, sprinkle with salt, and place on a platter with a garnish of parsley. Serve warm, at room temperature, or cold with the sauce on the side.