How to Make It
In a large bowl, whisk together the flour, baking soda, and salt. Set aside.
Using an electric mixer, beat the butter and sugar on medium-high until smooth. Add the egg and beat until fluffy, about 2 minutes. Beat in the vanilla.
Reduce mixer speed to low. Gradually add the flour mixture, mixing until just incorporated (the dough will be stiff). Shape into a disk and refrigerate, wrapped, for at least 1 hour and up to 3 days.
Heat oven to 350° F. Divide the dough in half. On a floured surface, roll each piece out ¼ inch thick. Cut into 2-inch squares. Transfer to parchment-lined baking sheets and refrigerate until firm, 10 to 15 minutes.
Bake, rotating the baking sheets halfway through, until just beginning to brown, 12 to 15 minutes. Cool slightly on the baking sheets, then transfer to wire racks to cool completely.
Dip one half of each cooled cookie into the chocolate, allowing any excess to drip off. Place on parchment-lined baking sheets, sprinkle with the peppermints, and refrigerate until the chocolate is set, 25 to 30 minutes. Store the cookies in an airtight container at room temperature for up to 3 days.