Heat the oven to a high roasting temperature. Cut each scrubbed potato into thick wedges. Soak the wedges in cold water for about 15 minutes, then dry them very well; this helps them become crisp. Toss with olive oil, garlic powder, paprika, onion powder, salt, and pepper.

Arrange the wedges in a single layer on a lined baking sheet, leaving a little room between them. Roast, turning once, until browned outside and tender inside. Sprinkle Parmesan over the hot wedges and return them to the oven for a few minutes so the cheese melts and crisps. Finish with parsley.