Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, add the butter, powdered sugar, and peppermint extract. Mix on low until combined and there are no butter chunks (do not over mix).
Add the dry ingredients: almond flour and coconut flour and mix on low until combined into a stiff dough, it should feel like play dough in your hands.
Using your hands, form the dough into 24 balls and place on each parchment-lined baking sheet, you'll have 12 cookie dough balls per sheet. Flatten them slightly so they are 2 to 2 1/2-inches in diameter. These don't spread much, because of the almond flour and coconut flour mixture, so the size you make the dough balls is about the size the cookies will be.
Bake for 13 to 15 minutes or until the edges and bottoms are lightly golden brown. Sprinkle with cane sugar immediately after coming out of the oven. Allow to cool completely on the baking sheets.
Once the cookies have cooled, in a double boiler add about 80% of the dark chocolate. Melt until it reaches 115°F on a chocolate thermometer, then remove from heat and add in the remaining dark chocolate and stir to combine. Let rest until chocolate reaches 91°F. Alternatively, you can melt all the chocolate in a microwave safe bowl, doing 30 second intervals, and stirring between each one. You don't need to temper the chocolate, it's just optional!
Dip half the cookies into the dark chocolate and place on parchment paper.
Allow to set and cool completely, you can stick in the fridge for about 1 hour.
Store in a cool dry place or in the fridge for up to 7 days.