They grill them, and then they cover them with a mid size stainless steel "cover;" they make cover specificially for that purpose but I think they (Jacksonhole) uses something like a Ice Cream Sundae "bowl" or some such similar item.
Multiple cooking methods are common. At my place we will cover items (burgers (rarely), tuna melts (usually), etc. to get cheese to melt. We make a skillet Mac N Chz that starts on the stove top and finishes in the oven. In professional kitchens its come to move things around. E.g., take a par-baked 1/2 chicken, broil it for a few minutes under the Salamander (e.g., a professional broiler) — basically to give it a nice color — then pop the whole thing including the pan into the oven for 10 minutes (or so) to finish the cooking, put it on a plate, sauce it up and serve.