Mix the cuts by hand: Put the minced short rib, chuck and brisket into a large bowl and mix with your hands, adding the fat a little at a time. Stop the moment it's combined, since overmixing is what makes burgers bouncy.
Shape and rest: Divide into four portions, roll into balls and press gently into patties, then leave them at room temperature for about 10 minutes before cooking.
Season and fry: Season both sides with plenty of salt and pepper. Heat a dash of vegetable oil in a large frying pan until hot, then fry for 5 minutes each side for medium, or 8 to 10 for well done. A preheated barbecue works the same way with the patties brushed in oil.
Make the Char Siu butter: While the burgers cook, preheat your overhead grill to high. Mix the softened butter with the honey, hoisin, black bean paste and garlic, and spoon a tablespoon over each cooked patty. Optional, but this is the juiciest version of this burger.
Double cheese under the grill: Lay two slices of cheese on each patty, over the butter if using, and flash under the hot grill until melted and drooping.
Toast and build: Lightly toast the halved buns, then layer lettuce, tomato and gherkin under each cheese-topped patty and crown with the lids. Serve immediately.
