Wash squash, discard seeds, and slice into 1" thick rings, then slice each ring in half.

Peel carrots and cut into 1" chunks, cut cauliflower into large florets, cut onion into chunks, and cut larger mushrooms in half.

Place all veggies in large bowl.

Combine olive oil, garlic, and spices in a separate small bowl.

Pour over veggies and toss to coat.

Prepare a rimmed baking sheet with cooking spray and arrange seasoned veggies in a single layer, leaving room for sausage links.

Add sausage to pan and cut a small slit in each to avoid bursting.

Bake at 400 degrees for 40 minutes, flipping veggies and sausage over halfway through.

Remove pan and top veggies with Parmesan, then return to oven and roast for another 5 minutes or until Parmesan is melted.