Make a double batch of hot chocolate---some to eat and some to freeze. Fill the popsicle molds almost to the top and finish them off with marshmallows. Yum!
Turn off heat and slowly, stirring constantly, add evaporated milk and vanilla.
Transfer hot chocolate to another container to allow to cool in the refrigerator.
When the hot chocolate is cool enough, pour into popsicle molds about 3/4 of the way to the top. Fill the molds with marshmallows almost to the top, pushing them down to be slightly moistened so they will stick together when freezing.
Freeze for several hours or overnight. Run the molds under hot water to loosen the popsicles. Remove and serve.