This is the easiest, peasiest (OK, actually no peas...), most affordable-est sheet pan dinner you'd ever like to see. Naturally gluten free (as long as your sausage is).
Spray rimmed baking sheet with cooking spray. Add sausage and veggies to a large bowl, then drizzle with olive oil, add seasonings, and toss to coat.
Spread seasoned sausage and vegetables out on the baking sheet and roast at 425 degrees for 40 minutes, stirring halfway through.
Remove from oven and immediately sprinkle with Parmesan (optional, yet recommended).
Notes
You can substitute chicken sausage and sweet potatoes to lighten up the recipe a little, if desired. Be sure to cut the potatoes fairly small as shown here, so that they cook through.