Stir the sweetened condensed milk and whole milk together and microwave for 60 seconds. Stir until combined well and add the vanilla.
Break the cookies into 1 inch pieces, and place chunks from 1 1/2 cookies into each mold. (Press down a bit, but don't stuff it down too much.)
Pour the milk mixture into each mold- leaving a teeny gap on the top as popsicles will expand as they freeze. Add popsicle sticks and freeze until solid.