Freeze the beef, wrapped in a plastic wrap, for 1 hour, or until it is firm but not frozen solid, and with a very sharp knife cut it across the grain into 1/8-inch-thick slices. Arrange the slices about 3 inches apart on sheets of plastic wrap, cover them with additional sheets of plastic wrap, and with a rolling pin, roll the slices thin, testing the first rolled slice to make sure it is no too thin to be lifted from the plastic without tearing. Roll up the sheets of plastic loosely and chill the beef for at least 1 hour or up to 3 hours.

In a blender puree the artichoke hearts with the vinegar, the lemon juice, and salt and pepper to taste, add the oil in a stream and 2 tablespoons warm water, and blend the mixture until it is emulsified.

Divide the beef slices among 4 chilled plates, lining the plates with a single layer of the slices, and mound the arugula and the Parmesan curls in the center of each plate. Sprinkle each serving with the pepper to taste, drizzle some of the dressing over each serving, and serve the remaining dressing separately.