Preheat oven to 425℉. Line a large sheet pan with parchment paper, foil, or lightly grease it.
Prepare the potatoes. Place the halved or quartered potatoes on the sheet pan. Drizzle with olive oil and spring with salt and pepper. Toss to coat.
Roast the vegetables for 15 minutes.
Remove the sheet pan from the over and add the sausage and broccoli.
Season the sausage and broccoli with olive oil and salt and pepper. Toss to coat.
Continue roasting for 20-25 minutes or until the potatoes are tender and golden brown, the broccoli is roasted and the sausage is heated through and lightly browned.
Serve immediately while hot.