Prepare a large, rimmed baking sheet and spray with vegetable oil. Adjust oven rack to lowest position and preheat oven to 450 degrees.
Cut cauliflower into 2-inch pieces. Toss with oil in a large bowl.
Stir in a smaller bowl until thoroughly combined: Parmesan, cornstarch, thyme, salt and pepper.
Add Parmesan mixture to cauliflower and oil and toss until well coated.
Pour contents of bowl onto prepared baking sheet.
scraping out any remaining Parmesan from bowl with rubber spatula. Spread cauliflower and cheese evenly and where possible, flip florets cut side down.
Roast cauliflower for about 15 minutes. Flip florets and continue to roast about 5 minutes longer until cauliflower is tender and spotty brown.
