It's hard to make such a big burger in a pan or on a griddle. Especially with the cheese in the middle (this is at least twice as big as a typical Jucy Lucy). There are two options. One is lightly cooking the outside in an iron skillet then putting it in the oven. The other is to heat up a metal pan on your griddle just slightly bigger than the burger, then covering the burger while cooking it. If you build up a good amount of steam before cooking it then you will steam it through while it sits on the griddle.

EDIT: MvF did a thing about a place that makes them the second way: http://www.youtube.com/watch?v=ZxkpTE7xfz4