Beat butter in a large bowl with an electric mixer at medium speed about 30 seconds. Add sugar and salt and beat until combined. Beat in egg yolk and peppermint extract. Beat in flour and cocoa. Shape dough into a 6-inch roll. Wrap in plastic wrap or wax paper. Chill until firm enough to slice, about 2 hours, or freeze about 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Cut roll into 1/8- to 1/4-inch slices. Arrange 2 inches apart on an ungreased baking sheet.

Bake in the preheated oven until edges are firm, 7 to 8 minutes. Cool on the baking sheet on a wire rack (cookies are too delicate to remove until cooled).

Microwave semisweet chocolate and candy melts in a small bowl, stirring twice, until melted and smooth, 1 to 2 minutes.