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When ready to cook, start the Traeger on Smoke with the lid open until a fire is established (4-5 minutes).
Whisk the mayonnaise and green peppercorn mustard in a small bowl; cover and refrigerate until serving time.
In a small mixing bowl, combine the Dijon-style mustard, horseradish, Worcestershire, and thyme leaves. Coat the outside of the tenderloin with the mixture, including the ends. Season on all sides with Traeger Prime Rib Rub or salt and pepper.
Lay the meat directly on the grill grate and smoke for 1 hour. Transfer to a cutting board and wrap tightly with foil.
Increase the temperature of the Traeger to 350 degrees F. In the meantime, pour a thin film of olive oil on a rimmed baking sheet and arrange the bread slices on it in a single layer. Press down on each piece to make sure it gets coated with the oil. Toast until lightly browned, about 15 minutes, then turn over with a spatula to brown the other side, about 10 minutes more. Transfer to a cooling rack.
Increase the temperature of the Traeger to High (400 to 450 degrees F). Allow 15 minutes for the grill to come up to temperature. Remove the foil from the beef tenderloin and return the meat to the grill grate. Grill, turning as needed with tongs, until the tenderloin is done to your liking—135 degrees F for medium-rare, about 20 minutes. (Insert an instant-read meat thermometer in the thickest part of the meat.)
Transfer the tenderloin to a cutting board and let it rest for 5 minutes. Carve against the grain into very thin slices. (If desired, you can chill the tenderloin, tightly wrapped in plastic wrap, for up to 24 hours before slicing.)
To assemble the crostini, lay a slice or two of tenderloin on a piece of toasted bread. Top with a dollop of the mayonnaise-mustard sauce and a piece of parsley. Enjoy!