In a large bowl, combine the cake mix, shortening, butter, egg, water and vanilla until well blended. Divide into four equal parts. Between waxed paper, roll one part into a 10-in. x 6-in. x rectangle. Remove one piece of waxed paper and invert dough onto a ungreased baking sheet. Score the dough into eight pieces, each 3-in. x 2-1/2-in. Repeat with remaining dough.
Bake at 350° for 8-10 minutes or until puffed. Immediately cut along the scored lines and prick holes in each piece with a fork. Cool on wire racks.
Cut ice cream into 16 slices, each 3-in. x 2-1/2-in. x 1-in. Place ice cream slice between two chocolate cookies; wrap in plastic wrap. Freeze on a baking sheet overnight. May be frozen for up to 2 months.