Dip Peep in egg whites, then roll in crumbs. Dip in egg whites again and roll in crumbs for a second coating. Dip in egg whites a third time and roll in shredded coconut. Pat coconut into the breading. Make sure the Peep is well coated so it ends up with an impenetrable graham cracker-shell armor. Heat oil to 350 degrees F and fry Peeps one at a time, rolling it over once one side has browned. Fry until the Peep is golden brown or starts to leak, about 30 seconds. Place finished Peeps on paper towel-lined plate. Allow to cool a bit before eating, but eat it while the innards are still molten.
