Combine first 5 ingredients (through crystallized ginger) in a bowl.
Beat next 4 ingredients (through brown sugar) with an electric mixer at medium speed. Add dry ingredients; mix until just blended. Wrap in plastic; chill 2 hours.
Preheat oven to 350°. Coat 2 baking sheets with cooking spray.
Fill 2 bowls: 1 with cold water, 1 with granulated sugar. Dampen hands in water; form a 1-inch ball of dough. Roll in sugar; place on baking sheet. Make cookies; place 3 inches apart and lightly flatten tops. Bake 13–15 minutes, rotating sheets halfway through. Remove from oven; cool 2 minutes. Transfer cookies to a wire rack to cool completely.