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TO COOK THE BEEF:
Preheat oven to 260 degrees C.
Place the beef on baking sheet and pat the outside dry with a paper towel.
Mix the unsalted butter and mustard together in a small bowl and spread the mixture over the beef with your hands.
Sprinkle evenly with the salt and pepper.
Roast in the oven for exactly 22 minutes for rare and 25 minutes for medium-rare.
Remove the beef from oven, cover lightly with aluminum foil, and allow it to rest at room temperature for 20 minutes. Remove the strings and slice fillet to preferred thickness.
TO MAKE DRESSING:
Whisk together all ingredients in a small bowl. Serve at room temperature.
TO MAKE THE SANDWICH:
Cut the bread into ¼" thick slices.
Spread 4 of the slices thickly with the Mustard Horseradish Sauce.
Top with slices of beef and arugula and sprinkle with salt and pepper.