In large measuring cup, whisk pudding mix and milk until thoroughly combined. Set aside to soft set, about 5 minutes.
Cut or break six cookies in half and set aside. Pour remainder of package in 1-gallon bag, seal it and use rolling pin to crush cookies.
Spoon layer of cookie crumbs in bottom of each jar, reserving some for topping. Top with layer of vanilla pudding. Cut one banana in half lengthwise and slice. Put layer of bananas on top of pudding. Top bananas with another layer of pudding. Repeat with remaining ingredients.
Refrigerate until ready to serve. To serve, top with whipped topping and sprinkle with crushed cookies. Serve each with broken cookie half.