Preheat the oven to 500 degrees F. (Be sure your oven is very clean!)
Place the beef on a sheet pan and pat the outside dry with a paper towel. Spread the butter all over the beef with your hands. Sprinkle the beef evenly with 1 1/2 teaspoons salt and 1 1/2 teaspoons pepper. Roast 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 15 minutes. Remove the strings and slice the fillet about 1/4-inch thick.
Open the baguettes lengthwise but not all the way through. Spread the bottom halves generously with the truffle butter. Top with a layer of sliced beef and sprinkle it with salt and pepper.
Using a vegetable peeler, shave the Parmesan into thin shards and scatter the shards over the sliced beef on each sandwich. Finish with a sprinkling of arugula leaves. Fold the tops of the sandwiches over, cut each baguette diagonally in 3 or 4 sandwiches, and serve right away.
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