Preheat the oven to 350 degrees. Grease a cookie sheet.
In a small bowl, mix the cake mix, egg, cream cheese and butter until it is all well combined. The mixture will be very thick.
Take about 2 Tablespoons of cookie dough. Wrap the dough around the peppermint pattie until it's covered completely. Place on cookie sheet.
Repeat with the remaining peppermint patties and dough.
Bake at 350 degrees for 10-11 minutes.
Allow the cookies to cool for 4-5 minutes on the cookie sheet, then transfer them to a wire rack to cool completely.
Store in an airtight container.
