In a large bowl, with mixer at slow speed, beat flour, sugar, butter, molasses, applesauce, egg, cinnamon, baking powder, ginger, cloves, nutmeg, baking soda, and salt until well mixed. Cover and refrigerate 1 hour.

Preheat oven to 350°F On a lightly floured surface, working with half of the dough at a time, roll 1/8 inch thick. With floured cookie cutters, cut dough into shapes. Using a metal spatula or pancake turner, place cookies 1/2 inch apart on greased cookie sheets. Reroll trimmings and continue to cut shapes. Bake 8 minutes, or until very lightly browned. Transfer cookies to racks to cool completely.