Cream the butter, shortening and sugar together, beating for about two minutes until the mixture is light and fluffy. Beat in the vanilla and egg.
Beat in the flour, cocoa, baking powder and salt until everything is well combined.
Form the dough into a disc shape and wrap it in plastic wrap. Refrigerate it for at least three hours or overnight.
For baking, preheat the oven to 350 degrees.
Line two baking sheets with parchment paper and set them aside.
To form the mice, scoop out about one tablespoon of dough. Roll it into a ball and then shape it into a teardrop shape.
Add an M&M to the pointed end to create a nose for your mouse, and then stick two halves of a peanut into the top of the dough to form ears. (Make sure they're stuck in about halfway so they'll stay better.)
Place the cookies about one inch apart on the prepared sheets.
Bake for 10 minutes and then let the cookies sit on the baking sheet for about five minutes before carefully poking a piece of lace licorice into each cookie to create tails. (I used my meat thermometer to make a small hole to make it a little easier to get my licorice to stick into the cookie.) Let the cookies cool completely, and then store them in an airtight container.