Place the beef on a 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 the oven, cover it tightly with aluminum foil, and allow it to rest at room temperature for 20 minutes. Remove the strings and slice the fillet thickly.
To make the sandwiches, cut the bread into 1/4-inch 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. Spread 4 more slices of bread very lightly with butter and place, butter side down, on top of the beef.
Mustard Horseradish Sauce:
Whisk together the mayonnaise, mustards, horseradish, sour cream, and a pinch of salt in a small bowl. Serve at room temperature.