Step 1: In a bowl, cream together softened butter and sugar until light and fluffy.
Step 2: Beat in egg, vanilla extract, and 1/2 teaspoon peppermint extract until combined.
Step 3: Whisk together flour, cocoa powder, and salt in a separate bowl.
Step 4: Gradually mix dry ingredients into wet ingredients until a dough forms.
Step 5: Roll dough into a log about 1.5 inches in diameter, wrap in plastic, and chill for 1 hour.
Step 6: Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Step 7: Slice dough into 1/4-inch thick rounds and place on prepared sheets.
Step 8: Bake for 10-12 minutes until firm, then cool completely on wire racks.
Step 9: Melt chocolate chips and shortening in a double boiler, then stir in 1/2 teaspoon peppermint extract.
Step 10: Dip each cooled cookie into melted chocolate, coating fully, and place on parchment to set.