Whisk the egg white and wine together in a bowl. Add the bread crumbs, turkey, onion, salt, and pepper. Stir to mix. Form into 1/2-inch thick patties.
Grill for about 5 to 6 minutes then turn over and grill for another 5 to 6 minutes. Once you flip the patties, set the pineapple slices on the grill. Cook the pineapple for 3 minutes then turn over and cook for another 3 minutes.
Put the patties on the buns and place a slice of pineapple on top.