1. Preheat the oven to 425°F. Place a sheet pan in the oven while preheating.
2. Cut the onion, apples, and potatoes into a 1-inch dice.
3. In a large bowl mix together the olive oil, mustard, and seasonings, then add the chopped apples, onion, and potatoes to the bowl and toss to coat.
4. Poke a few holes into the sausage links with a fork.
5. Carefully pull the sheet pan from the oven and add the apple mixture to the hot pan. Nestle the sausage links among the mixture and place back into the oven.
6. Cook for 25-35 minutes, until potatoes are fork tender and internal temperature of sausage is 160° F, turning the sausages and stirring the apple mixture halfway through cooking.
7. Turn the oven to broil and cook for 5 minutes more.
8. Remove the sausages to a platter. Drizzle the apple cider vinegar over the cooked apple mixture (the vinegar adds a little tartness and accentuates the flavors) and toss, then place the mixture around the sausages on the platter to serve.