In a mixing bowl, whisk together the instant banana pudding mix and cold milk until smooth and slightly thickened, about 2 minutes.
Add the prepared pudding mixture to a high-speed blender along with the ripe bananas and maple syrup (if using).
Blend until the banana mixture is completely smooth and creamy.
Carefully pour the popsicle mixture into a popsicle mold, leaving a little room at the top for expansion while freezing.
Insert a popsicle stick into each mold. If needed, cover the mold with plastic wrap first to help hold the sticks upright.
Freeze overnight, or until the homemade banana popsicles are completely solid.
To remove the popsicles, run warm water over the outside of the popsicle mold for a few seconds before gently pulling them out.
Serve immediately or store in an airtight container, freezer bag, or plastic popsicle packaging bags in the freezer.