Preheat oven to 350 degrees Fahrenheit. Cover a cookie sheet in parchment paper (if desired).
In a medium bowl, stir together flour, baking powder, baking soda, and salt.
In a separate medium bowl, beat together sugar and butter until fluffy. Beat in flax egg and vanilla.
Add the dry ingredients into the wet and beat until combined (no streaks of flour remain).
Spoon out dough, 1/2 Tablespoon at a time, and roll into balls. Roll each ball of dough in garnishing sugar, then chill the dough balls in the fridge for about 20 minutes.
Remove from the fridge and arrange on cookie sheet two-three inches apart from each other (they will spread).
Bake at 350 degrees Fahrenheit until edges turn golden, about 7-10 mins.
Remove cookies from oven. While the cookies are still warm, press a peppermint chocolate into the center of each cookie.