IN a large skillet, heat 1 tablespoon of the oil over medium heat. Add the shallots; cook until shallots begins to soften, 3 to 4 minutes. Add the mustard seeds and cook until lightly toasted and fragrant, 1 to 2 minutes. Add the remaining oil, curry powder, salt, and pepper; stir until combined. Add the cabbage and apples; and stir to combine in the mustard seed mixture. Cook, stirring occasionally, until cabbage and apples are tender, about 10 minutes.
MEANWHILE, preheat a grill or grill pan over medium-high heat. Grill bratwurst, turning once halfway through, until 165°F, 10 to 12 minutes. Let bratwurst rest for 5 minutes, then slice each diagonally into 1-inch pieces.
DIVIDE the slaw between 4 serving plates. Top with bratwurst, drizzle with the sauce, and sprinkle with parsley.