How to Make It
Whisk together flour, cocoa powder, and salt.
Combine butter, sugar, and vanilla in a food processor and process until creamy and evenly incorporated. Add flour mixture and pulse until mixture is uniform but still crumbly, scraping down sides of bowl as needed. Turn dough out and knead until smooth. Divide dough in half and form each into a square-edged log. Wrap in plastic wrap, squaring off edges, and refrigerate until firm, at least 1 hour or up to 2 days.
Preheat oven to 350°F with racks in upper and lower thirds. Line 2 baking sheets with parchment paper. Slice dough ¼-inch thick and transfer to the prepared sheets. Bake until dry around the edges, 10 to 12 minutes, rotating top to bottom and back to front. Let cool completely on sheet.
Transfer shortbread to a wire rack set over a baking sheet. Heat chocolate in a microwave-safe bowl, stirring every 30 seconds, until melted and smooth; stir in peppermint extract. Dip tops of cooled cookies in chocolate mixture. Turn right-side up and place on rack. Sprinkle with crushed peppermint candies and a little salt. Refrigerate until chocolate is set, 15 to 20 minutes. Store in an airtight container at room temperature for up to 2 days.