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1
Cover work surface with plastic wrap and put steak on it with a short side of steak nearest you. Holding a sharp knife parallel to work surface and beginning on a long side, using short slicing motions, butterfly steak by cutting it horizontally almost, but not all the way, in half, then open it like a book.
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2
Cover steak with a double thickness of plastic wrap (about 2 feet long) and, using the flat side of a meat pounder (or using a rolling pin), gently pound meat 1/4 inch thick.
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3
Discard top sheets of plastic wrap and turn steak on plastic wrap so grain of meat is running left to right, then rub 1 tablespoon oil onto steak and sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Arrange prosciutto in a slightly overlapping layer on steak, then cover with cheese.
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4
Beginning with side nearest you, using plastic wrap as an aid and pressing slightly on filling, roll up steak tightly, then skewer steak, crosswise, at 1-inch intervals. Using a sharp knife, cut between skewers to make 1-inch-thick pinwheels. (End pieces will be about 1 1/2 inches thick. Trim if desired. For more about how to form beef pinwheels, see
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5
.)
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6
Prepare grill for cooking over medium-hot charcoal (moderate heat for gas). If using a charcoal grill, open vents on bottom of grill, then light charcoal. When charcoal turns grayish white (about 15 minutes from lighting), hold your hand 5 inches above grill rack to determine heat for charcoal as follows:
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7
Hot: When you can hold your hand there for 1 to 2 seconds
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8
Medium-hot: 3 to 4 seconds
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9
Low: 5 to 6 seconds
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10
If using a gas grill, preheat burners on high, covered, 10 minutes, then, if necessary, reduce to heat specified in recipe.
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11
Grill pinwheels, cut sides down, on a well-oiled rack, turning over once (use a metal spatula to loosen), until beef is well browned outside but still pink inside and cheese is beginning to melt, 6 to 8 minutes total.
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12
Toss arugula with remaining 2 tablespoons oil and 1/4 teaspoon salt in a large bowl. Serve on a platter, topped with pinwheels.
