Wash and dry all produce. Preheat the oven to 400 degrees. Halve, peel, and finely dice half the onion. Drain and finely chop the pineapple. Finely chop the chives. Peel the carrot, then grate it with a box grater.

Heat a drizzle of oil in a large ovenproof pan over medium heat. Add the diced onion. Cook, tossing, for 2-3 minutes, until softened. Add the pineapple. Cook, tossing, for 2-3 minutes, until lightly caramelized and jammy, adding 1 Tablespoon water if necessary. Season with salt and pepper. Remove from the pan and set aside in a large bowl. Rinse out any browned bits from the bottom of the pan.

Meanwhile, toss the cabbage in a medium bowl with the chives, carrot, 11/2 Tablespoons mayonnaise, 1 Tablespoon white wine vinegar, and 1 teaspoon sugar. Season generously with salt and pepper.

Form the patties: Form the ground beef into two equally-sized patties. Season generously with salt and pepper.

Heat a drizzle of oil in the same pan over medium-high heat. Add the patties to the pan. Cook 2-5 minutes per side, until cooked to desired doneness (2 for rare and 5 for well- done). Top each patty with Monterey Jack cheese, covering the pan to allow it to melt. Meanwhile, split the buns and place in the oven to toast 3-5 minutes.

Assemble and serve: Thinly slice the remaining onion. Spread the buns with the remaining mayonnaise and top with a burger, carmelized-pineapple relish, and a few slices of onion (if desired). Serve alongside the red cabbage slaw and enjoy!