Cake: Prepare two 8" or 9" cake layers according to directions on devils food cake mix box. Cool for approximately 40 minutes before frosting.
Meanwhile make Chocolate Curls: With vegetable peeler, shave along side of each Andes mint lengthwise to equal about 1/2 cup of curls. Chop broken pieces and reserve for use in frosting (about 1/3 cup).
Frosting: In large bowl with mixer on medium speed, beat the cream cheese until smooth, then lower the speed and slowly mix in the non-dairy whipped topping. Fold the Andes thin mints pieces into the cream.
Assembly: Place one cake layer on serving plate; top with half the frosting and spread evenly. Place the second cake layer on top and spread remaining frosting on top of cake. Sprinkle top with Andes Mint Curls.
Cover and refrigerate cake if not serving immediately.