1. In a stand mixer fitted with paddle attachment, cream butter and sugar until light and fluffy. Add vanilla and salt and beat until combined. Add flour and beat until flour is just incorporated. Shape dough into a disk, wrap in plastic wrap, and chill for 30 minutes.
2. On a lightly floured surface, roll out dough and use a floured cutter to cut out shortbread people. Gather scraps, re-roll, and cut until all dough has been used. Transfer to a baking sheet, placing cookies 1 to 2 inches apart, and chill for 30 minutes.
3. Preheat oven to 350 degrees. Once cookies are chilled, bake until they just begin to set, 10 to 12 minutes. Let cool slightly on baking sheet, then transfer to a wire rack to cool completely.
4. Meanwhile, place chocolate in a heatproof bowl over simmering water. Stir until chocolate is melted and smooth. Remove from heat.
5. Dip bottom half of each cookie in melted chocolate, then place on a tray lined with parchment or wax paper. Before chocolate hardens, sprinkle each cookie with peppermint candy.