Cream together sugar, butter, egg, and vanilla.
Add flour, cocoa, salt and peppermint extract and combine until smooth dough forms.
Press into a thick slab, cover and refrigerate at least 30 minutes.
Preheat oven to 350 degrees.
Break of a section of the dough and roll out between two pieces of parchment paper to 1/8th of an inch thick. Make sure the bottom piece of parchment paper can fit on your baking sheet.
Peel off top piece of parchment paper.
Use cookie cutter to cut shapes out in pairs, about 1/2 inch apart.
Peel off excess dough away from shapes, lift up the parchment paper with cookies and transfer directly onto baking sheet.
Bake for 8-10 minutes until edges are set and centers are not glossy. Centers will feel soft, but will set when cool.