Pre-heat oven to 350 degrees and line baking sheets with parchment paper.
Add flour, cinnamon, nutmeg, ginger, baking soda, and salt to a medium sized bowl and mix.
Add butter and sugar to a bowl of stand mixer (or to a large bowl) and cream with paddle attachment or hand mixer.
Beat in egg and then add maple syrup, vanilla, and then add applesauce.
Add flour mixture and then use a spatula to mix in.
Add in oats and fold in shredded carrots and with spatula.
Add small balls of dough (2-3 inches) on parchment paper. Keep in balls or flatten if a flatter cookie is desired. Leave at least 1 inch between doughs because they will not spread much.
Bake for 10 minutes and then rotate baking sheets in oven and bake for another 10 minutes.
Meanwhile, make cream cheese frosting.
Remove cookies from oven and add to cooling rack.
Once cookies are cooled, add frosting.
Serve and enjoy! Or store in an airtight container for up to a week, or freeze for up to 3 months.