Preheat oven to 375° F. Line a cookie sheet with parchment paper.
In a medium bowl, whisk together flour, baking soda, baking powder, cinnamon, nutmeg and salt. Set aside.
In a large bowl of a stand mixer, mix sugar and shortening together until well combined. Add egg and applesauce. Mix well, about 2 minutes. With the mixer on low, slowly add in dry ingredients. Mix until combined.
Drop heaping tablespoonfuls of batter on lined cookie sheet. Cookies should be about 1 1/2-inches in diameter.
Bake at 375° F for 8-10 minutes or until the edges start to turn golden brown. Allow cookies to cool on sheet for a few minutes before transferring them to a rack to cool completely.
While cookies are cooling, prepare frosting.
Caramel Frosting
In a medium saucepan, combine butter, heavy cream and brown sugar over medium heat. Stir occasionally until mixture just begins to boil. Remove from heat and stir in vanilla. Let the mixture cool and then stir in the confectioners' sugar.
Using a spoon, spread frosting over cookies. Sprinkle with cinnamon if desired.
Notes
Cookies may be stored in an airtight container at room temperature for up to a week. Frost cookies before storing them.