Preheat oven to 375 degrees F.
Add the butter to a shallow baking pan and place in the oven to melt.
Add the cut potatoes to a bowl of water to soak for a few minutes.
In a resealable gallon-sized bag or a shallow baking dish, add the flour, Parmesan cheese, and salt and pepper to taste.
Add cut potatoes to the bag a few at a time and shake. The moisture from the water soak will help the coating stick. Alternatively, roll the potatoes in the coating in a baking dish. Remove potatoes and lay them on a flat side in the pan with the melted butter. Repeat with remaining potato wedges.
Bake potatoes for 20 - 25 minutes, then turn them to the other flat side and bake an additional 20 - 25, or until golden brown.