Preheat your BBQ to medium-high heat (about 375°F).
In a frying pan over medium-high heat, add the oil and the onions and cook until the onions are translucent but not starting to brown. Add the apples, vinegar, and brown sugar and cook, stirring occasionally, until the mixture is soft and starts to caramelize, about 10 minutes. Turn down the heat to medium-low and season to taste with salt and pepper.
Meanwhile, grill the sausages, turning them occasionally, until they’re golden brown and cooked through, about 12 minutes. Remove from the grill and add them to the sauté pan with the onion and apple mixture, still over medium-low heat. Allow the sausages to rest on top of the onion and apple mixture while you prepare the buns.
Cut the buns open and generously spread them with the grainy mustard. (You can also toast the buns first, if you like.) Add one sausage to each bun and pile high with the caramelized apples and onions. Serve immediately.
