In a large bowl, beat margarine, brown sugar, applesauce and egg until smooth.
In a medium bowl, combine flour, baking powder, cinnamon and salt. Add to the applesauce mixture, stirring by hand just until you have a soft dough. Divide the dough in half, wrap each half in plastic and refrigerate for at least an hour or until well chilled.
When ready to bake, preheat oven to 375 degrees. Roll dough 1/8 inch thick between two sheets of waxed paper. Cut with a 2 1/2 inch cookie cutter or glass rim, and place 1 inch apart on a cookie sheet that has been lightly sprayed with nonstick spray.
Bake for 10 - 12 minutes, until edges are golden. Bake 5 minutes longer for darker golden, crispier cookies. Transfer to a wire rack to cool.