In a medium bowl, add your ground pork, apple sauce(or grated apples), your chopped caramelized onions, salt, pepper, and garlic powder. You can also add some optional rosemary and breadcrumbs. mix well
Form four equal patties. You want to form the patties thin, as they will shrink up while they cook. You will need to cook them in a large skillet to make them all fit, but if they don't all fit, you can cook them in two batches.
Cook the patties for 3.5 minutes on each side. Once you flip them over, add a slice of white cheddar and let it melt completely as the burgers finish cooking. I cook the burgers on the second side for 3.5/4 minutes. If your burgers are thicker, you may want to keep it on the heat a little longer per side.
Put the burgers on a plate so that they can rest for 5-10 minutes.
Toast the buns while the burgers are resting.
Top each burger with a some of the caramelized onion mixture. You can also add some thin slices of apples as a topping too!