Combine brown sugar and shortening in a large bowl; beat with a mixer at medium speed until light and fluffy. Add molasses and egg; beat well. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 5 ingredients (through salt), stirring with a whisk. Add flour mixture to sugar mixture; beat at low speed just until blended. Cover and freeze 1 hour.
Preheat oven to 375°.
Place water in a small bowl. Place granulated sugar in another small bowl. Lightly coat hands with cooking spray. Shape dough into 1-inch balls. Dip one side of each ball in water; dip wet side in sugar. Place balls, sugar side up, 1 inch apart, on baking sheets coated with cooking spray. Bake at 375° for 8 minutes. Remove from pans; cool on wire racks.