Prep the grates of your Commercial 4 Burner Gas Grill by cleaning and oiling and preheat for indirect heat by turning up 2 of the 4 burners (2 of 3 if you have a 3 burner grill).
Mix the brads and beef in a large bowl and season with salt and pepper. I found some delicious Irish garlic brats at my local market and used those for this mix. If you can't find those, mix in some minced garlic and parsley. Form into large patties, just under ½” thick, with a dimple in the center, and allow to rest in the fridge for 20 minutes before grilling.
Braise the onions with the stout in a small iron skillet, stirring occasionally, about 20 minutes. Braise the cabbage in a larger skillet (it will wilt substantially), with the broth and red wine vinegar, covered, about 20 minutes as well. Increase heat and remove lid to cook off any excess liquid if needed. This can be done on the grill, using the side burner, or over the grate if desired.
Meanwhile, When ready to grill, place the patties on the cooler side of the grill and cook until an instant read thermometer reads 160, flipping once, halfway through cook time. Top with cheese and allow to rest on a covered platter.
Combine the Honey Dijon Mustard and mayo in a bowl, add some freshly ground black pepper, if desired.
Arrange the toasted buns out for assembly. Slather with the honey dijon mayo, layer with fresh greens, a juicy grilled patty, cheese, crispy bacon, braised cabbage and onions, and topped for devouring.