Preheat oven to 350 degrees F (175 degrees C). Lightly grease baking sheets.
In a large bowl, mix together the cake mix, butter, vanilla extract, eggs, chocolate chips, and butterscotch chips into a dough.
Roll dough into 2-inch balls and place them onto the prepared baking sheets. Bake for 10 minutes in the preheated oven. (Do not over bake, as the cookies need to be set, but still soft.) Let cool on the baking sheet for a few minutes before removing to finish cooling on wire racks.
Using an ice cream scoop, mold the softened ice cream into a ball about the size of the cookies. Place scoop of ice cream between two cookies and gently press together. Fill all of the cookies, lay out on a baking sheet, and place in the freezer to harden.