Using a stand mixer, hand mixer, or whisk, cream together the butter, applesauce, and maple sugar until smooth, or for 3-4 minutes.
Beat the egg, molasses, and gingerbread spices into the creamed mixture until smooth.
In a separate bowl, combine the flour, baking soda, and salt. Add these dry ingredients to the wet ingredients and whisk until thoroughly combined.
Let the dough chill in the fridge for 1 hour.
Preheat your oven to 350 degrees Fahrenheit and line two baking sheets with parchment paper.
Lightly dust a clean surface with flour and roll out the dough until approximately 1/8 inch in thickness. Use a cookie cutter to cut out the cookies and place them on the sheet, with ample space between each cookie as they will expand as they bake. Continue to reshape and roll out the scraps of dough until all of it has been cut into cookies.
Bake the cookies in the oven for 10 minutes, or until firm.
Let cool on the baking sheets for 3-5 minutes and then transfer to a cooling rack.
Store in an airtight container for up to five days.