Make vanilla pudding according to package. Stir in ½ cup of Baileys Irish Cream. Fold in Oreo cookies.
Make chocolate pudding according to package. Stir in remaining ½ cup of Baileys Irish Cream.
Transfer each pudding mixture into a pastry bag. Layer and fill popsicle wells. Insert popsicle in center of each well. Transfer to freezer for 6-8 hours. (Time will vary according to freezer setting and how full freezer is).
To release popsicles from well, run hot water on the outside of popsicle for 2-3 seconds. Remove popsicle and serve immediately.