Pour the chocolate milk evenly into popsicle molds. Freeze for 2 hours, or until solid.
In a small bowl or measuring cup, stir together the cooled brewed coffee, half-and-half, and sugar until the sugar dissolves.
Pour the coffee mixture over the frozen chocolate layer.
Insert popsicle sticks and freeze again for 2 hours, or until firm.
In another bowl, stir together the heavy cream, sugar, and vanilla extract.
Pour the vanilla cream mixture over the frozen coffee layer.
Freeze for 4 hours, or until completely firm.
To unmold, run the outside of the popsicle molds under warm water for a few seconds, then gently pull out the popsicles.
