To cook on a griddle, heat a cast-iron griddle (yes, a flat-top griddle!) to medium high and preheat the oven to 350 degrees F. Oil the griddle with vegetable oil, put the patties on the griddle and cook on one side for 6 to 8 minutes. Transfer the patties to a baking sheet and continue to cook in the oven until the meat registers 155 degrees F. Add a little more oil to the griddle and add the pineapples and onions. Cook the pineapple rings on one side until charred and easily released to be flipped; cook on the other side until grill marked. Cook the onions until tender and charred, about 15 minutes. Remove to a plate. Lower the temperature to medium. Brush the buns with the butter, put them on the griddle buttered-side down and grill until toasted but still shiny, 1 to 2 minutes