Preheat oven to 350 ° F.
Combine flours, cocoas, xanthan gum and baking soda in a small bowl and stir with a whisk.
Combine brown sugar, butter, applesauce, vanilla extract and peppermint extract in a medium bowl and beat with a mixer at high speed for 2 minutes.
Whisk egg replacer and water together and then add to sugar mixture. Beat. Add flour mixture and beat low until well blended.
Using a small cookie scoop (1 1/2 tsp) scoop out dough onto a cookie sheet, leaving an inch in between.
Bake for 8-10 minutes or until looks dry. Don’t over bake. You want them chewy. Let cool on a cookie sheet for a few minutes then remove and cool completely on a wire rack.
Alternatively, to make more of a traditional thin mint style cookie:
Spread dough onto a sheet of plastic wrap sprayed with cooking spray. Roll up the sheet until the dough is in 6 inch log shape. Coat hands with cooking spray and coax it if needed. Freeze for about an hour. Take out and immediately cut into thin slices with a sharp knife. Place on cookie sheet and inch apart and bake for 10-12 minutes. Remove and cool on wired racks.
3/4 cup superfine brown rice flour
1/4 cup potato starch
1/4 cup tapioca starch
You can also just use 1/2 cup of regular cocoa. I just like the dark chocolate flavor.
You may prefer to use less peppermint extract. I think especially if you use all regular cocoa you may need to reduce to 1/4 tsp. I like the combination of dark cocoa and minty flavor.