Preheat oven to 375°F. Line a rimmed baking sheet with parchment paper or spray with nonstick cooking spray. Set aside.

Cut sausage and vegetables into relatively uniformly-sized pieces - about 1/2 to 1 inch. Cut harder vegetables such as potatoes and cauliflower into slightly smaller pieces, and faster-cooking vegetables into larger pieces - the goal is to have everything done at around the same time.

Place all vegetables and the sausage into a large zip-top bag or a large bowl and toss with the olive oil, salt, pepper and spices to coat. Spread evenly onto the prepared baking sheet and roast for 30-40 minutes, stirring halfway through, until vegetables are cooked and sausage is browned.

Serve topped with fresh parmesan cheese and/or garnished with fresh parsley, if desired.