Combine cake mix, melted shortening, cake flour, and egg in a large bowl. Add water 1 tablespoon at a time, mixing after each addition, until a dough forms.

Flatten dough into a disc and wrap with plastic wrap. Chill for 2 hours.

Preheat oven to 350 degrees F.

On a lightly floured surface, roll out 1/4 of the dough to 1/16 of an inch thick.

Cut out cookies using a spice container lid with a 1 1/2 inch diameter.

Arrange the cut dough rounds on a cookie sheet that is sprayed with a light coating of non-stick spray or is lined with a Sil-Pat.

Bake for 8 to 10 minutes. Remove wafers from the oven and cool on pan for 1 minute. Transfer cookies to a wire rack and cool completely.

Combine chocolate chips with peppermint extract and shortening in a large microwave-safe glass or ceramic bowl.

Heat on 50% power for 1 1/2 minutes, stir gently, then heat for an additional minute. Stir once again. If chocolate is not a smooth consistency, continue to microwave chocolate in 30 second intervals, then stirring, until smooth.

Use a fork to dip each wafer in the chocolate. Tap the fork on the edge of the bowl so that the excess chocolate runs off. Place the cookies on a waxed paper lined baking sheet. Refrigerate until firm.