Preheat the oven to 400°F.

Line a baking sheet with parchment paper. Set aside.

Cut the squash into 3/4-inch cubes and arrange in an even layer on the prepared baking sheet.

Drizzle the squash with the olive oil. Sprinkle with the dried thyme, salt, and black pepper. Use a rubber spatula to toss the squash until it is evenly coated in the oil.

Roast the squash on middle rack of oven for 30 minutes. Open the oven and sprinkle the Parmesan cheese evenly over the squash. Roast until the squash is fork-tender and the cheese is melted and lightly browned, 5-10 minutes longer.

Check to see that squash is done. Remove from oven or add time as needed.

Sprinkle fresh thyme leaves over the squash, if desired. Serve immediately.