In a large mixing bowl, combine the cake mix, melted butter, and extracts. Beat on low speed until combined. Then add the egg and combine until a soft dough forms.
Add the cream cheese and mix in gently until combined.
With a wooden spoon, stir in the peppermint crunch pieces and chocolate chips.
Refrigerate dough for at least 30 minutes (don't skip this step).
Roll the dough into 36 balls.
Bake on a cookie sheet at 350 degrees for 9 to 10 minutes. Do not over bake. The cookies will appear very soft and look undercooked. Let them sit on the hot cookie sheet for 2 minutes, then gently remove them with a spatulas to a cooling rack.
Let them sit until completely cool. Store in a sealed container.