For the marinade: Combine all the ingredients in a medium saucepan over medium-high heat. Bring to a simmer, then remove from the heat. Reserve 1/4 cup of the marinade for the slaw. Transfer the remaining marinade to a shallow baking dish and let cool completely.
For the burgers: Divide the meat into 4 equal portions (about 6 ounces each). Shape each portion with your hands into a round patty, about 3/4 inches thick. Use your thumb to make a divot in the center of each burger. Transfer to the shallow baking dish with the marinade, cover and refrigerate at least 10 to 15 minutes and up to 2 hours.
For the cabbage slaw: Combine the cabbages, carrots, green onions, cilantro and sesame seeds in a medium bowl. Add the reserved 1/4 cup marinade and season with salt and pepper to taste. Let sit at least 15 minutes before serving.
To finish the burgers: Heat a griddle or large cast-iron pan over high heat. Add the canola oil and let heat until it begins to shimmer. Remove the burgers from the marinade, season with salt and pepper and place in the pan. Cook the burgers, basting with the marinade and flipping once, until golden brown on both sides and cooked to medium doneness, about 8 minutes total.
Place the buns cut-side up on a baking sheet, brush the cut sides with some canola oil and toast in the oven until golden brown, 4 to 5 minutes.
Meanwhile, make the gochujang "ketchup": Whisk together the gochujang, orange juice and honey in a small bowl and set aside.
Place the burgers on the bottom buns. Top with the gochujang "ketchup", a spoonful of the slaw, cilantro leaves and the top buns and serve immediately.