Cut the pineapple into 1/2" thick rings. Cutting it into rings makes it less likely they'll fall through a BBQ grate. You will probably want to cut them into smaller pieces once they've finished grilling. You can start by cutting the pineapple into smaller pieces if you're not using a BBQ.
Make the burger patties by mixing the ground pork, breadcrumbs, garlic, lemon juice, mayo, mustard, egg, and salt & pepper with your hands. Form into slider-sized patties (make the burger patties' diameters slightly larger than your slider buns as they will shrink a bit), and make a small divot in the middle so they stay flat after being cooked.
Oil grill grate and then pre-heat grill to medium-high heat. Add patties and cook for 4-5 minutes each side (depending on thickness of patties) or until they're cooked through. If you're adding cheese, add the cheese with one minute to go until they're done so it melts but doesn't burn.
Grill the pineapple rings for about 3 minutes per side.
(Optional) If desired, you can toast the buns. Spread butter on them and then place them on the grill for 30 seconds or until they're toasted as you like.
Assemble the sliders by adding the sauce, burger patty, and the pineapple. Enjoy!