Cut scrubbed potatoes in quarters lengthwise, then into 1 1/2-inch chunks. Place potato chunks into a gallon-sized, zip-top plastic bag.
Add remaining ingredients (except for Parmesan) to the bag. Close and shake to coat potatoes with the seasonings and oil.
Coat a large baking sheet with cooking spray. Pour potatoes onto the baking sheet.
Bake potatoes for 15 minutes, then remove from oven and flip and stir them with a metal spatula. Return to the oven for another 10 minutes, then repeat the flipping and stirring, returning them to the oven for a final 10 minutes of cooking and browning.
Remove from oven, sprinkle with Parmesan cheese if desired, and serve immediately.