Preheat oven to 425 degrees and spray a rimmed baking sheet with cooking spray.
Add sweet potato, broccoli, mushrooms, onion, and smoked sausage to a large bowl. Drizzle with olive oil and add all seasonings, then toss until sausage and veggies are well coated.
Arrange sausage and vegetables in a single layer on your prepared baking sheet (it's OK if they're a little crowded; they'll shrink down).
Roast at 425 degrees for 30 minutes, stirring halfway through, or until sweet potatoes are softened and everything else is nicely roasted.
Notes
This sausage & sweet potato sheet pan dinner recipe is also naturally gluten free.