Preheat the oven to 400 degrees F (200 degrees C). Line a 12x18-inch sheet pan with parchment paper.
Place bell pepper pieces and chopped onion in the bowl of a small food processor or blender and pulse several times into small, uniform pieces. Transfer vegetables to a large mixing bowl and add garlic.
Combine liquid smoke, low-sodium soy sauce, rice vinegar, sesame oil, and egg in a small bowl; stir briskly to combine. Mix in bread crumbs, stirring until moistened. Add to vegetables. Add ground beef and season with salt and pepper. Mix all ingredients with your hands until evenly combined.
Form ground beef mixture into twelve 3-inch patties and space evenly on the prepared sheet pan.
Bake in the preheated oven until desired doneness is achieved, 8 to 10 minutes per side.
While the patties are baking, prepare the pineapple slaw. Drain pineapple tidbits and reserve 1 tablespoon of the juice. Combine pineapple tidbits, shredded cabbage, and green onions in a salad bowl.
Stir mayonnaise, rice vinegar, reserved pineapple juice, salt, and pepper together in a bowl for the dressing. Toss pineapple slaw with the dressing.
Slice Hawaiian bread rolls horizontally and place a cooked patty on each bottom half. Add 2 to 3 tablespoons pineapple slaw, and top with the other roll half. Garnish each slider with a pineapple chunk, secured with a toothpick.
