Caramelize the onions
Add the onions, olive oil, and salt to a small skillet and place over the fire at medium-low heat. Cook, stirring occasionally, until the onions are soft and beginning to caramelize, about 20-25 minutes.
Form the burger patties
Meanwhile, peel & grate the apple on the large holes of a cheese grater. Mix with the ground beef and salt, then form into six patties.
Grill the burgers
Cook the patties over medium-high heat, about 3-4 minutes on each side. Toast the buns, then build the burgers, topping each with the cheddar, caramelized onions, and any other condiments you wish.
Make ahead at home
Form the patties at home, omitting the salt. Prepare the caramelized onions at home on your stovetop. Store the patties and the onions in separate airtight containers in your cooler until ready to cook. Salt the patties right before grilling at your campsite and reheat the onions in a small skillet until warmed through.