First, let's make the binder.
Place the torn bread in a food processor and pulse until you have coarse crumbs.
Transfer the crumbs to a large mixing bowl and set it aside.
Without cleaning the food processor, add the macadamia nuts, cilantro, and garlic. Pulse until everything is finely chopped.
Add the rinsed and drained black beans, hoisin sauce, salt, and pepper. Use several on/off pulses until the beans are coarsely chopped and the mixture starts to pull away from the sides of the bowl. Be careful not to over-process into a paste!
Scrape the bean mixture into the bowl with the bread crumbs.
Add the lightly beaten egg white and mix everything together with your hands or a spatula until just combined.
Divide the mixture into four equal portions and shape them into 1/2-inch-thick patties.
Place the patties on a tray or plate, and brush both sides with olive oil.
Cover and chill in the refrigerator for at least 1 hour. This step is crucial to help them firm up!
While the patties are chilling, whisk together all the for the Lime Mayonnaise in a small bowl.
Cover and refrigerate until you're ready to serve.
Preheat your grill to medium heat and lightly grease the grates.
Place the chilled patties and the drained pineapple slices directly on the grill.
Cook for 8 to 10 minutes, flipping once halfway through, until the patties are heated through and have nice grill marks, and the pineapple is lightly browned and caramelized.
During the last minute or two of grilling, place the hamburger buns, cut-side down, on the grill to lightly toast them.
Assemble your masterpieces!
Spread a generous amount of Lime Mayonnaise on the toasted buns, then add a black bean patty, a grilled pineapple slice, and any other favorite toppings.
Serve immediately!
Don't skip the chill!
Chilling the patties for at least one hour is the most important step for ensuring they are firm enough to hold their shape on the grill without falling apart.