Toast the sesame seeds in a small pan until a light golden colour. Remove from the pan and set aside.
In the same pan, combine the gochujang, soy sauce, mirin, sesame oil, dark brown sugar, 3 crushed garlic cloves, ground black pepper, and chilli flakes. Reserve the rice wine vinegar at this stage. Stir over medium heat until the sugar dissolves—the sauce should be heated through but need not come to a boil.
Add approximately 1 tablespoon of rice wine vinegar, tasting as you go.
Stir in 3 tablespoons of the toasted sesame seeds, reserving the rest to sprinkle over the cooked burgers. Set aside the gochujang BBQ sauce while you prepare the patties.
Divide the pork mince into either 4 portions of 250g or 5 portions of 200g.
Form each portion into a ball, throwing it between your hands a few times to compact the meat slightly. Shape into discs slightly wider than the buns you're using, creating a shallow well in the centre of each patty. Chill for at least 30 minutes before cooking.
Cook the patties on a BBQ, teppanyaki grill, or frying pan over medium to medium-high heat, flipping at least once, until almost cooked through.
At around 65°C internal temperature, turn the heat to high and start basting the patties generously with the gochujang BBQ sauce, flipping and basting each side. Aim for three coats. The target final internal temperature for ground pork is 75°C—bearing in mind the internal temperature will continue to rise for a minute or two after removing the patties from the heat.
Remove from the heat and sprinkle with the reserved toasted sesame seeds.