Butterfly the meat by making a lengthwise cut down the center, cutting to within 1/2 inch of the other side, but not through it. Spread open. Cut from the center, horizontally, to the outside edge and within 1/2 inch of the other side of meat. Repeat on opposite side of center. Spread these sections open to make one thinner piece.
Rub top side with 2 tablespoons olive oil. Sprinkle with rosemary. Arrange prosciutto or dried beef on top to cover completely. Arrange spinach over prosciutto to cover completely.
Beginning at a short side, roll up meat. Tie in three or four places with heavy string. Brush with additional olive oil and sprinkle with the peppercorns, if you like.
In a covered grill, arrange the preheated coals around a drip pan for indirect grilling. Test for medium heat above the drip pan. Place the prepared meat on the grill rack over the drip pan. Cover and grill the meat for 3/4 to 1 hour for the venison, 1 to 1-1/4 hours for pork or until a meat thermometer inserted into the thickest part of meat registers 140 degree F for medium-rare venison or 155 degree F for well-done pork.
Remove the venison or pork from the grill and place on serving platter; cover and let stand for 10 to 15 minutes before serving. (The temperature of the meat will rise 5 degree F as it stands.)
To serve, remove string from the meat. Carve the meat into 1/4- to 1/2-inch-thick slices, being careful to keep the spiral intact. Makes 6 servings.
To test the temperature of the preheated coals, place your hand above the coals at the height the food will be cooked. Start counting and if you need to remove your hand after 4 seconds, the coals are medium.