Combine teriyaki sauce, minced garlic, gingerroot, and parsley in a medium bowl. Add pork; gently mix. Shape into 4 meatballs. Cover with plastic wrap and refrigerate for 30 minutes. Meanwhile, toss pineapple slices with teriyaki sauce; marinate at room temperature for 10 minutes.

Preheat a charcoal or gas grill for direct cooking over high heat. Place a large cast-iron griddle on grill rack to preheat. Remove meatballs from refrigerator; sprinkle with kosher salt and black pepper. Place meatballs 1 inch apart on hot griddle. Sear for 30 seconds. Smash burgers to ¼-inch thickness using a large spatula. Cook 6 to 8 minutes or until edges begin to brown. Turn over burgers; cook 4 to 6 minutes more or until burgers reach 160°. During the last 3 to 5 minutes, place pineapple slices on grill grate; grill until charred and softened.

Butter and toast brioche hamburger buns. To assemble, brush bun bottoms with honey barbecue sauce; top each with a burger, avocado slices, pickled jalapeno slices, crispy onions, additional barbecue sauce, and bun top.