Preheat oven to 400°.
Melt butter in a medium saucepan over medium heat. Add sugar, water, salt, nutmeg, ginger, and cinnamon; bring to a simmer. Cook 5 minutes, stirring frequently. Discard cinnamon stick. Combine sugar mixture and potato wedges in a large bowl; toss well to coat. Arrange potato mixture on a large jelly-roll pan coated with cooking spray. Bake at 400° for 40 minutes or until tender, stirring after 20 minutes.