Combine the slaw ingredients into a mixing bowl, set aside or refrigerate until ready to use.
In a small dish, combine ketchup and hoisin, set aside. In another small dish combine mayo and gochujang, set aside.
In a medium mixing bowl, combine beef, garlic, ginger, Worcestershire, soy, sesame, and salt and pepper. Divide mixture into 4 equal sections and form into patties.
Preheat a skillet or grill over medium-high heat. Cook or grill burgers to desired doneness. I do about 3-4 minutes per side if you have a sizzling hot grill/skillet. I usually cook less on the second side, as it will continue to cook when you remove from heat.
While the burgers are cooking, fry the eggs in a lightly buttered or greased large flat skillet over med heat, about 2-3 minutes per side, depending on desired doneness (runny yolk vs. cooked), remove from heat.
Spread bottom toasted buns with hoisin ketchup, then add the burger, then a slice of bacon torn in half, topped with some kimchi slaw, then the fried egg. Spread the top toasted bun with gochujang mayo and place on top. Grab a napkin and enjoy!
I used a local brand of kimchi that is carried in some specialty stores, the brand is You Betcha Kimchi. Otherwise you may find other brands in the refrigerated section of your local store, or at an Asian foods grocery store.
I use Miracle Whip in the slaw dressing, the added sweetness and tang really makes the slaw, I recommend using that vs. regular mayo for added flavor.
The gochujang in my store is by the ketchup in a small bottle.
I was super happy to see brioche buns in my local grocery store in the bakery area, not the bread isle. It wasn't made at the store's bakery, but it was displayed in that area. It's just a great restaurant style soft bun that toasts nicely and is perfect for burgers.