Take the sausage links and lightly, diagonally score them tops and bottoms. Place on the sheet pan, along with chopped potatoes and broccoli. Add oil and seasonings and gently toss until everything is evenly seasoned. Spread into an even layer, without anything overlapping.
After the first 15 minutes of roasting, remove the sheet pan. Pour the honey mustard sauce over everything and gently move and toss everything around until evenly coated. Return to the oven and bake an additional 10-15 minutes.