Preheat oven to 350 degrees.
In a medium bowl, combine flours, cocoa powder, flax seed, baking powder, baking soda, salt and cinnamon. Mix well and set aside.
In another medium bowl, cream the butter and sugars together until smooth. Add the applesauce, Greek yogurt, vanilla and egg. Mix well.
Add the flour mixture 1 cup at a time to the Greek yogurt combination. Mix until combined, be careful not to over mix.
Drop by rounded teaspoonfuls onto an ungreased nonstick baking tray.
Bake for 12-15 minutes until browned.
Cool on the tray for 5 minutes before moving to a wire rack to col completely.
While cookies are cooling, prepare icing by mixing powdered sugar and milk.
Pour icing into heavy duty plastic bag (it will be thick) and carefully snip the small end of the bag.
Squeeze icing out and make 3 concentric circles.
Next, trace lines outside each circle to form a spider web.