Preheat a gas or charcoal grill to medium heat (about 375°F).
Prepare the cabbage and onion topping:
Heat the vegetable oil in a frying pan over medium heat. Add the sliced onion and sauté until softened, 5 to 7 minutes. Add the sliced cabbage, a handful at a time, and continue cooking, stirring often, until the cabbage wilts and reduces in volume, 3 to 4 minutes longer.
Sprinkle the brown sugar over the mixture, add the vinegar, and season with salt and pepper. Continue cooking for about 10 minutes, stirring often, until the cabbage and onions are tender and golden. Taste and adjust the seasoning if needed, then remove from the heat.
Prepare the honey mustard sauce:
While the cabbage and onions cook, combine the coarse grain and Dijon mustard in a small bowl. Stir in the honey and set aside.
Grill the bratwurst:
Oil the grill grates and add the bratwursts. Grill, turning frequently, for 5 to 6 minutes, or until the casings are crisp and lightly browned. Transfer them to a plate, cover loosely with foil, and set them aside to keep warm.
Toast the rolls and serve:
Toast the rolls until golden, then spread them with some honey mustard. Add the bratwurst, top with the cabbage-onion mixture and serve.
Notes
ABOUT THE BRATWURST: Our recipe calls for fully cooked bratwurst; however, if you prefer to use fresh bratwurst, please increase the grilling time accordingly and cook them to an internal temperature of 160°F.MAKE AHEAD INSTRUCTIONS: Both the honey mustard sauce and cabbage and onion mixture can be made up to two days in advance. Reheat the cabbage and onions in the microwave just before serving.