For the horseradish sauce:
In a small bowl, mix together all ingredients. Start with half of the horseradish and add more for a desired level of heat. Place in the fridge for at least 30 minutes and up to a day before using.
For the sandwiches:
1. Preheat a grill or oven to 450 F.
2. Cover the beef roast liberally with your favorite steak rub (alternatively, use kosher salt and freshly ground black pepper). Place it in a roasting pan with a rack with the beef in the rack and the broth in the pan. Let it rest on the counter for an hour and come to room temp.
3. Place the roast in the grill or oven. After 10 minutes, lower the temperature to 250 F. Continue to cook the roast until it hits an internal temp of 130 F to 135 F. Remove the roast and allow it to cool for 20 minutes.
4. Pour the beef stock jus into a saucepan (run it through a fine mesh strainer if you have one) and place on low heat.
Slice the beef as thin as you can. Pile it on the bottom bun and top with the horseradish sauce. Dip the top bun partially into the jus before putting it on top of the sandwich. For even more flavor, dip the beef in the jus before adding it to the sandwich or serve the sandwich with a side of jus for dipping.