Place ground bison in a bowl. Add two tablespoons of the BBQ rub and mix. Divide the meat into eight patties.
Divide the cheese into four parts. Sandwich one cheese part between two patties and seal the edges to form a burger. Coat all of the side of burger with additional rub. Salt and pepper both sides of the patties.
Grill the burgers to desired doneness. Grill pineapple slices and cut side of buns.
Mash avocado thoroughly with 1⁄2 teaspoon of fresh lime juice.
Combine the Sriracha, mayonnaise and remaining lime juice with a pinch of garlic salt. Salt and pepper to taste.
To build the burger, spread avocado on the bottom bun. Place the burger next.Top it with a pineapple slice. Add a lettuce leaf and top that with crispy jalapeños. Spread sriracha mayonnaise on the top bun and place it on the burger.