In bowl of an electric mixer fitted with paddle attachment, combine butter, sugar, salt, peppermint extract, and egg. Beat on medium-high speed until light and fluffy, scraping bowl as necessary. Reduce speed to low and gradually add flour, scraping bowl as necessary, until a soft dough forms. Divide dough into two portions, form into 1-inch-thick disks, and wrap in plastic wrap. Refrigerate for at least 15 minutes or until ready to use.

Heat oven to 350°. Working with one dough at a time, roll dough out on a lightly floured work surface until ¼-inch-thick. Use a 1.-inch round cutter to stamp out cookies. Place on parchment-lined baking sheet and bake until set, about 8 minutes, rotating halfway through baking time. Cool on a wire rack.

Combine chocolate and 4 tablespoons butter in medium bowl set over a pot of simmering water. Stir until melted and smooth. Sandwich a dab of chocolate between each cookie. Drizzle with remaining chocolate, moving rapidly from left to right. Combine a drop of peppermint extract with ¼ cup of sanding sugar and sprinkle over cookies.