Start your Grill on ''smoke'' with the lid open until a fire is established in the burn pot (3-4 minutes). Preheat to 300F.
In a large bowl, mix together the ground beef, ground pork, eggs, barbecue sauce, and seasoning until combined. Do not over mix as this will cause the meat to be tough after cooking. Split the mixture into two equal parts.
Melt the butter in a pan over medium heat and saute the onion mushrooms until golden.
In a cast iron pan, flatten one half of the meat mixture into the bottom, taking care to work meat slightly up the sides of the pan. Sprinkle in half of the bag of cheese. Pour in onion mixture and top with the rest of the cheese.
On a clean work surface, mold the second half of the meat mixture into a circle and cover the filling to complete the burger. Make sure that the top and bottom meat patties are secured together so that the filling cannot be seen.
Place the cast iron pan in the Grill for 1 hour - 1 hour 15 minutes, or until the internal temperature reaches 160F. Crank up the to ''HIGH'' and open the flame broiler. Flip the burger out of the cast iron pan onto the grates and sear each side for 5 minutes, to get those beautiful grill marks.
To serve: You can make an enormous burger like we did, or you can cut it like a pie into slices to be served on regular hamburger buns with your desired condiments.