In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar until creamy and smooth, about 2-3 minutes. Scrape down the bowl and turn the mixer on medium speed. Add the eggs, one at a time, beating until combined after each addition. Add the vanilla, and mix just until combined.

Scrape down the bowl, ensuring that the butter mixture is well mixed. Meanwhile, in a medium bowl stir together the gluten free all-purpose flour, baking powder, salt, and dark chocolate. Add the flour mixture to the butter mixture, and turn the mixer on low speed. Mix until just combined.

Place the dough in between two pieces of parchment paper. Roll into a ¼ inch thick disk and place in the freezer for at least 1 hour. Remove the dough from the freezer and let sit at room temperature for 10-15 minutes.

While the dough is thawing, preheat the oven to 350°F. Once the dough has thawed slightly, cut into circles, using a 2-3 inch cookie cutter. Place the cookie dough cutouts on a parchment-lined baking sheet, and place in the freezer for 5 minutes.

Re-roll the dough and freeze for 10-15 minutes. Remove from the freezer and cut out shapes with remaining dough. Place the dough in the freezer for 5 minutes. Immediately after removing the cut out cookie dough from the freezer, place in the oven. Bake for 8-10 minutes, turning halfway through baking.

Once cookies are removed from the oven, let cool for 5 minutes before moving to a cooling rack to cool completely.

While cookies are cooling, make the icing. In a small bowl, whisk together powdered sugar, cocoa powder, and salt. Add vanilla and 2 tablespoons of milk. Begin whisking, and add more milk, 1 tablespoon at a time, until the icing is the consistency of honey. Ice the cookies as desired. Once iced, sprinkle cookies with a bit more sea salt.