When the grill is preheated, place baking dish with onions as well as the burger patties on the grill. Close the lid and cook for 5-6 minutes.
Meanwhile, spread butter on the inside of each bun on both the top and bottom halves. Set aside.
Flip the burgers and onions, close the lid again and cook for an additional 4-5 minutes.
Add the buns butter side down directly onto the grates of the grill while the onions and burgers continue cooking for 2-3 minutes. Remove all items when buns are lightly toasted and burgers are fully cooked. (If there isn't enough room on the grill, finish cooking burgers and onions and toast the buns when they've finished.)
To assemble, apply a layer of the cheese spread to the bottom bun, then the burger, the grilled onions, sauerkraut, and lastly a layer of stone ground mustard on the top bun.
Serve and enjoy!