Preheat the oven to 350ºF and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the dry ingredients. Add flax egg, syrup, oil and vanilla to the bowl and mix together until it forms a thick, pliable dough.
Transfer the dough to a parchment lined surface. Place another sheet of parchment on top and roll the dough until it's about 1/8" thick. Using a gingerbread man cutter, cut out the shapes and place them on the baking sheet. Reroll the dough and continue to cut out your cookies until the dough has been used up.
Bake the cookies for 10 minutes. Remove from oven and allow to cool completely before frosting.
For the frosting, whisk together the sugar and milk. Transfer to a piping bag or squeeze bottle.
Once the cookies are cool, pipe the frosting onto the cookies in whatever design you like. Enjoy!