Set up a grill for direct cooking over high heat. Melt the butter in a large skillet on the grill or side burner.
Add the onions and cook until soft, about 10 minutes, stirring occasionally. Cover and cook about 10 more minutes. Uncover the skillet and simmer about 5 minutes.
Reduce the heat to medium and oil the grates. Grill the brats on the grates 4 to 5 minutes per side.
Lightly toast the rolls on the grill. Serve the hot brats on the rolls, smothered with the onions and topped with mustard.