Preheat oven to 350℉ using middle rack.
Melt butter for brushing on top of buns after bake and line a cookie sheet with parchment paper.
Knock down dough and portion into 12 pieces. Take out 1 piece at a time, keeping the remainder in the fridge (they will likely stick back together some).
Lightly flour work surface to roll out dough.
Roll out dough ball to about 7" in diameter, keeping edges slightly thinner and the middle thicker. Layer ¼ cup meat mixture, ½ cup cheese, and another ½ cup meat mixture. This ensures that the cheese won't be on the bottom and soak through and make a soggy bottom.
(See images above in narrative) Pinching dough at opposite sides of the dough, gently stretch the dough and pinch ends together at the center. With one hand pinching the center together, gradually work your way around repeating this process. Once you have sealed off the burger, flip over so seal is face down and gently rock the dough under your palm to seal the burger..
Place burgers 1 at a time on a baking sheet lined with parchment paper. Repeat until you have 6 burgers to bake at a time.
Bake at 350℉ for about 30 minutes or until golden brown. Keep an eye on them around 20 minutes but you want the bottoms to be browning as well which takes a bit more time. Remove from oven and leave on tray for a 5-10 minutes before transferring to another surface to allow them to reabsorb some moisture.
Repeat process with remaining 6 dough balls to bake 6 more burgers. Use a second cookie sheet or a pizza stone. I wouldn't recommend using the same cookie sheet as the first batch because you need to let the first batch rest and you don't want to put the 2nd batch on a hot cookie sheet (this would affect the rising and you might get very large and overproved burgers.
Enjoy with hot sauce.