Unwrap Twix bars; place in resealable plastic bag. Seal and freeze 2 hours.
Meanwhile, to prepare cookies, preheat oven to 350 degrees F. In mixing bowl combine cake mix, eggs, oil, and water. Beat with electric mixer until combined. Drop dough by well-rounded teaspoons onto ungreased cookie sheets. Bake about 10 minutes or until tops are set. Cool 1 minute on cookie sheets. Remove cookies; cool completely on wire racks.
Spoon ice cream into large bowl. Let stand 10 minutes to soften slightly. Meanwhile, using flat side of meat mallet or a rolling pin, crush frozen Twix bars. Stir into ice cream; return to freezer until ready to use.
Spread marshmallow creme on flat sides of half of the cookies; place, creme side up, on a shallow baking pan. Using a small ice cream scoop, place some ice cream mixture onto flat sides of remaining cookies. Place on same baking pan, ice cream side up. Loosely cover and freeze for 2 hours or until firm.
Gently sandwich cookies together. Serve immediately or wrap each sandwich in plastic wrap and freeze in freezer container for up to 1 month. Makes about 14 sandwiches.