Set up your grill (see equipment options below) and get ventilation running before you cook anything, not after the smoke starts.
Preheat the grill or pan until a drop of water sizzles and evaporates within a second or two.
Lay the pork belly down first, unseasoned, spaced so pieces aren't touching. Let it render undisturbed for 2 minutes before flipping.
Once a pool of rendered fat has collected, push the pork to one side and add the garlic cloves, mushrooms and kimchi directly into that fat. Let them cook in it rather than on a dry section of the grill.
Flip the pork every 2 to 3 minutes, using scissors to snip thick pieces in half once they're mostly cooked, so more surface area gets direct contact with the heat.
Add the marinated beef last. Bulgogi-cut beef is thin and cooks in under 2 minutes per side — don't put it on until the pork is nearly done, or it will overcook waiting.
Add the onion wedges alongside the beef; they only need a couple of minutes to soften and pick up char at the edges.
Serve everything straight off the grill with lettuce and perilla leaves, ssamjang, the sesame oil dip, and rice, so people build their own wraps as they go.