Cook 4 strips of chopped bacon over medium heat until crispy, about 6-8 minutes. Stir in 1 cup of chopped kimchi and 2 tablespoons of brown sugar, then reduce heat to low. Cook for an additional 10-12 minutes, stirring occasionally, until caramelized and sticky.

In a large bowl, combine 1 pound of ground chicken with 2 tablespoons of gochujang, mixing well. Shape the mixture into 4 equal patties and cook on medium-high heat for 5-6 minutes per side until fully cooked.

While the patties are cooking, slice burger buns in half. Melt 2 tablespoons of butter in a skillet and toast the cut sides of the buns for 2-3 minutes until golden brown.

Assemble the burgers by placing a chicken patty on each bun half, topping with kimchi bacon jam, and placing the other half of the bun on top.