Plus: Ultimate Holiday Guide Fast Hors d'Oeuvres
Gently press the crushed pepper into the beef and sprinkle with the salt. Heat 1 tablespoon of the olive oil in a medium skillet. Add the beef and cook over high heat until well browned all over, about 10 minutes. Let cool, then refrigerate until chilled, at least 2 hours or for up to 2 days.
Preheat the oven to 350°. Brush the bread slices lightly on both sides with the remaining 2 tablespoons olive oil and arrange them on a large baking sheet. Bake for about 7 minutes, turning once, until lightly browned.
Spread about 1/4 teaspoon of the tapenade on each toast and set a halved arugula leaf on top. Using a sharp, thin-bladed knife, cut the chilled beef against the grain into 24 very thin slices. Arrange a slice of beef on each crostini and serve.
Before seasoning the meat in Step 1, dry the exterior thoroughly with paper towels. This will prevent the fat in the pan from sputtering and help the meat brown nicely.