In a skillet, cook the diced bacon over medium heat until crispy. Remove excess fat, leaving about 1 tablespoon in the pan.
Add the chopped onion and cook until softened, about 3 minutes.
Stir in the kimchi, brown sugar, and apple cider vinegar. Cook for another 5-7 minutes until the mixture thickens. Remove from heat and set aside.
In a large bowl, combine ground chicken, gochujang, soy sauce, garlic powder, ginger powder, and black pepper. Mix until just combined.
Form the mixture into 4 equal patties.
Heat the vegetable oil in a skillet over medium-high heat. Cook the chicken patties for about 5-6 minutes on each side, or until they reach an internal temperature of 165°F.
To assemble, place a lettuce leaf on the bottom half of each bun, add a chicken patty, top with kimchi bacon jam, and finish with sliced cucumbers. Place the top half of the bun on each burger.