In a bowl, mix together the mince, gochujang and pepper with a large pinch of salt until evenly combined. Shape into eight even balls and put on a tray. Tip the grated cheese onto a plate and gently shape it into four rough patties. Take one of the mince balls and gently press it into a flat patty that’s roughly 1cm thick (you also want it to be slightly bigger than the base of the buns, as it will shrink when cooked). Put one of the cheese patties into the centre, then return to the tray. Press a second ball of mince into a patty, put this on the cheese-topped patty, and gently press the edges together to enclose the cheese. Shape into a neat patty, return to the tray and repeat with the remaining balls of mince and cheese patties to make four cheese-filled burgers. Chill until needed.