Whisk together gluten-free flour, baking powder and salt in a mixing bowl. Set aside.
Melt unsweetened chocolate and butter in a microwave-safe bowl at high heat for 30 seconds or in a double boiler. Stir. Repeat until butter and chocolate are melted and smooth, about two minutes total. Stir granulated sugar and peppermint extract into melted chocolate. Add eggs and stir until combined. Add the flour mixture and stir until a very soft dough forms. Cover bowl with plastic wrap. Chill for at least two hours and up to three days.
Preheat oven to 350 degrees. Line a rimmed baking sheet with parchment paper.
Scoop dough, about two teaspoons each, and roll into balls. Roll dough into powdered sugar, making sure to coat the dough heavily in powdered sugar.
Place dough balls onto the prepared baking sheet, about 2 inches apart. Store dough in the refrigerator between batches.
Bake until cookies are crackled and set, about 12 minutes.
Cool cookies on a baking sheet for five minutes and then transfer to a wire rack to cool completely. Store cookies wrapped on the counter for up to three days or freeze up to three months.