Combine the butter and sugar in the bowl of a stand mixer fitter with the paddle attachment, or in a large mixing bowl with a hand mixer.

Stir at medium speed until the butter is light and fluffy. This should take about 1 minute.

Scrape the sides of the bowl and add the egg and extract. Mix an additional 30 seconds, or until the egg is fully incorporated.

In a medium sized measuring cup, stir together the flour, cocoa powder, and salt.

Pour the dry ingredients into the butter mixture and stir at medium speed until fully incorporated.

Divide the dough into two equal parts. Roll into a cylinder that is about 1-1/2 inches thick.

Wrap each roll in plastic wrap and transfer to the refrigerator for 2 hours, or up to 24.

Transfer the dough to the freezer 30 minutes before baking and preheat the oven to 350 degrees.

Working with one dough roll at a time, slice into 1/4 inch thickness.

Place onto a lined baking tray, roughly 1 inch apart.

Bake 10 minutes.

Allow to cool on the tray for 15 minutes and transfer to a cooling rack.

Combine the chocolate chips, peppermint extract, and shortening in a small glass bowl.

Heat for 1 minute in the microwave.

Stir until all of the chips have melted and are smooth.

Heat an additional 15 seconds if needed.

Use a fork to dip each cookie in the chocolate mixture.

Allow to cool until the chocolate has set.