Preheat oven to 350°. In a large bowl, combine the cake mix, shortening, butter, egg, water and vanilla until well blended.
Divide dough into 4 equal portion parts, and between sheets of waxed paper, roll 1 portion into a 10x6-in. rectangle. Remove top piece of waxed paper; invert dough onto a ungreased baking sheet. Remove second piece of waxed paper. Score the dough into 8 pieces, each 3x2-1/2 in. Repeat with remaining dough.
Bake until puffed, 8-10 minutes. Immediately cut along the scored lines and prick holes in each piece with a fork. Cool on wire racks.
Cut ice cream into sixteen 3x2-1/2x1-in. slices. Place 1 ice cream slice between 2 chocolate cookies; wrap in waxed paper. Repeat. Freeze on a baking sheet overnight.