Freeze banana slices in an airtight container or bag for 8-10 hours.
Place frozen banana slices, non-dairy milk, and vanilla into the bowl of a food processor fitted with the S blade. Pulse a few times to chop the bananas. Keep processing until bananas are thick, creamy, and smooth. Stop and scrape down sides, as needed.
Spoon the banana ice cream into popsicle molds. Add sticks and freeze until firm, at least 8 hours or overnight.
Prepare the chocolate shell by placing chocolate chips, coconut oil, and salt in a glass measuring cup. Microwave on 50% power for 30 second intervals, until chocolate is melted. Let cool to room temperature.
Remove pops from their mold and dip into the chocolate shell. Place on parchment or waxed paper and place back in freezer to allow ice cream to firm back up. Store pops wrapped in waxed paper in a bag or freezer proof container.