Beat together softened butter, sugar, peppermint extract and vanilla extract in a mixing bowl until combined and fluffy.
Sift flour and cocoa powder into a small mixing bowl. Stir in salt. Add the flour mixture to the butter mixture. Mix until a dough forms, scrape the side of the bowl as necessary while mixing to ensure the flour is mixing well with the butter.
Scrape the dough out of the bowl onto a piece of plastic wrap. Flatten it into a disk, wrap well and refrigerate for at least 30 minutes and up to 1 hour.
When the dough is firm but still malleable, take it out of the refrigerator and roll it into ¼” thick on a cocoa dusted surface. Cut with a 2” cookie cutter. Reroll the scraps and keep cutting out cookies until the dough is gone.
Place the cookies in a container or lined baking sheet and freeze for about 15 minutes while the oven is preheating.
Preheat the oven to 350°F.
When the oven is ready, place cookies on another parchment-lined baking sheet 1” - 2” apart and bake for 15 minutes.
Remove from the oven, let cookies cool on the baking sheet for 5 - 10 minutes before transferring to a wire rack to cool completely.
Combine chocolate, coconut oil and peppermint extract in a heatproof bowl, set it over a pot of simmering water, stir until chocolate is melted completely.
Dip cooled cookies in the melted chocolate using a fork, turn to coat both sides. Tap excess chocolate off and place coated cookies on a parchment-lined baking sheet. Allow chocolate coating to dry completely at room temperature or refrigerate to speed it up.