Preheat oven to 350°F. Grease, spray with cooking spray, or line a 10 x 15-inch jelly roll pan with parchment paper (see the notes below for a different size pan). Set aside.
In a medium bowl, whisk or sift together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt. Set aside. In a large bowl, use an electric mixer on medium speed to cream together the sugar and shortening until fluffy, about 3 minutes.
Add the eggs; beat to thoroughly combine. Add the applesauce and vanilla extract; mix until well combined.
Add the flour mixture to the applesauce mixture; mix just until combined.
Spread the batter in the prepared pan. Tap the pan gently on the counter a couple of times to release any large pockets of air.
Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean. Cool completely in the pan on a wire rack.
Once cool, dust with powdered sugar or spread with cream cheese frosting and dust with cinnamon, if desired.
Cut into squares and serve.