NOTE: These cookies are best enjoyed the day they are finished by being dipped in chocolate. The finished cookies can be stored in a sealed glass container at room temperature for about 2 days. For longer storage, seal the finished cookies tightly in a freezer-safe wrap or bag, and freeze for up to 2 months. Defrost at room temperature. The chocolate coating may bloom a bit over time, but it won’t affect the taste at all.
Prepare the cookies: Preheat your oven to 300°F. Line rimmed baking sheets with unbleached parchment paper, and set them aside.
In a medium-size, microwave-safe bowl, place the butter and chocolate and melt by placing the bowl in a double boiler or in the microwave in 30-second bursts at 60 percent power, stirring in between. Stir in the vanilla and peppermint extracts, and set the bowl aside. In a large bowl, place the flour, cocoa powder, baking soda, salt, and sugar, and whisk to combine well. Create a well in the center of the dry ingredients, add the melted chocolate mixture, and mix to combine. Knead the dough together, adding water by the quarter-teaspoonful as necessary to bring the dough together and make sure that it is pliable, and not stiff.
Place the dough between two sheets of unbleached parchment paper, and roll it out until it is about 1/4 inch thick. Cut out rounds that are about 1 3/4 inches in diameter, and place them about 1 inch apart from one another on the prepared baking sheets. Gather and reroll the scraps to cut out more cookies until you’ve used up the dough. Chill until firm to help the cookies bake more evenly.
Place the baking sheet in the center of the preheated oven and bake for 7 minutes, or until the cookies are dry to the touch. Remove from the oven, and allow the cookies to cool completely on the baking sheets.
Once the cookies the are cool, prepare the glaze: In a medium-size, microwave-safe bowl, place the chocolate and coconut oil and melt by placing the bowl in a double boiler or in the microwave in 30-second bursts at 60 percent power, stirring in between. Add the peppermint extract, and mix to incorporate. Allow the chocolate to sit at room temperature until it begins to thicken a bit. Line a rimmed baking sheet with unbleached parchment or waxed paper, and set it just to the side. Immerse the cookies, one at a time, in the glaze. Press down on the cookie with the tines of a fork, then flip it gently in the chocolate. Pull the cookie out of the chocolate by slipping the fork under it and bobbing the cookie on the surface of the chocolate a few times before pulling it along the edge of the bowl and carefully placing it on the prepared baking sheet. Allow the chocolate glaze to set at room temperature.