Start by making the bacon jam. Heat a skillet to medium heat. Add the diced white onion rings into the pan and a pinch of salt. As they warm, add the pieces of bacon. Cover and allow to cook for 3-4 minutes. Remove the lid and stir. Repeat this again until bacon is cooked and onions are caramelized. Turn off the heat and stir in the brown sugar.
Make the pork patties. In a mixing bowl, combine ground pork sausage, pieces of bacon, 1 egg, and seasonings. Mix until egg is dispersed and seasoning evenly folded in. Use a large cookie scoop divide meat mixture to make 4 burger patties of equal portions. Use your hands to flatten and shape the patties. They should be even sided pucks.
Drain the extra grease from the bacon jam and then transfer jam into a bowl. Wipe the skillet clean then reheat to medium heat. Once hot, place each breakfast sausage patty into the pan. Cover with a lid and allow to cook for 3-4 minutes. Remove the lid, use a spatula to flip the patties over. Cover again. Poke the burger patties with a meat thermometer. When they reach an internal temperature of 145F, transfer burgers to a paper towel lined plate (to absorb extra grease). Place a slice of cheese on each burger patty (use the skillet lid to cover & help melt if desired).
Fry the eggs. Clean the skillet out again (remove grease). Heat to medium heat. Once warm, crack 4 eggs into the pan. Cook evenly before flipping (over medium is my preference).
While the eggs are cooking, prep the buns. Set the oven to boiler. Grease the insides of the bun with cooking spray, swipe of butter or olive oil. Allow them to become golden in the broiler, then remove.
Assemble!! All of the burger parts are ready. Build: bottom bun, arugula, pork patty + cheese, avocado slices, bacon jam, fried egg, spicy aioli on the top bun. Adjust any toppings to your liking. Enjoy your epic burgers!!