The artichoke puree has a nice tarragon flavor that is a lovely complement to the beef. Use the remaining puree as a dip for crudités or pita bread.
2 teaspoons vegetable oil
48 slices cocktail rye bread
48 small arugula leaves
Puree artichokes in processor until almost smooth. Add mayonnaise, grated Parmesan, lemon juice, tarragon, lemon peel, garlic, nutmeg and cayenne. Process until well blended. Transfer to small bowl. Season with salt and pepper.
Heat oil in heavy large skillet over medium-high heat. Season steaks with salt and pepper. Add to skillet and cook to desired doneness, about 5 minutes per side for medium-rare. Transfer to plate. Cool. (Artichoke puree and steaks can be made 1 day ahead. Cover separately; chill.)
Preheat oven to 350°F. Using 1 1/2-inch round cookie cutter, cut 48 rounds from rye bread. Arrange rounds on large baking sheet. Bake until golden brown, about 8 minutes. Cool.
Spread 1 teaspoon artichoke puree on each rye round (save remaining puree for another use). Top with arugula leaf. Cut each steak across grain into 24 thin strips. Starting at 1 short end, roll up each beef strip. Place atop arugula. Garnish with shaved Parmesan.