In a large bowl, combine the pork, parsley, salt, garlic, 1/4 cup of the barbecue sauce and some pepper. Gently mix, then separate into 4 balls and rest at room temperature for 1 hour.
In a shallow dish, add the pineapple rings in one layer, then on each ring, add 4 slices of onion. Brush the tops with the remaining 1/4 cup barbecue sauce. Pour beer in the side of the dish up to the level of the pineapple. Rest at room temperature for 1 hour.
Heat an outdoor grill to medium high for direct and indirect heat (to cook on a griddle, see Cook's Note). Press the burgers into patties slightly larger than the buns. Place the burgers over the direct heat and cook on one side for 6 to 8 minutes. Flip to the indirect heat side of the grill and cook until the internal temperature reads 155 degrees F. Remove from the grill and lightly tent the burgers with loose-fitting aluminum foil for 5 minutes.
Meanwhile, shake the excess marinade off the pineapples and onions. Grill the pineapple rings on one side until charred and easily released to be flipped; grill on the other side until grill marked. Using a grill pan, cook the onions until tender and charred, about 15 minutes. Let rest for 5 minutes.
Brush the outside of the buns with the butter and place them on the grill buttered-side down. Grill until toasted but still shiny, 1 to 2 minutes. Build each burger starting with a bottom bun, a patty, a pineapple ring, some onions, a handful of plantain chips and a top bun.
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