If making banana nice cream, do this at least 2 to 3 hours before you want to eat ice cream sandwiches so the ice cream has time to firm up in the freezer. Add the bananas, strawberries, and a splash of milk to a food processor. Blend until smooth and creamy, stopping to scrape down the sides of the bowl as needed.
The nice cream will be similar to soft serve at this point. Scoop it into a freezer-safe container and freeze for about 2 hours. This will give you a firmer, scoopable texture for building the ice cream sandwiches.
Select a cookie flavor and bake the cookies. (See flavor pairing ideas in post above.)
Make the ice cream sandwiches:
If using homemade ice cream, once it's firm enough place one scoop on a cookie and top it with another cookie, gently pressing them together. Place ice cream sandwiches on a baking sheet or plate in the freezer. The amount of time needed in the freezer depends on how soft your ice cream is when you make the sandwiches. Check them after about 30 minutes.
If using store-bought ice cream, let it soften slightly. Then scoop it onto a cookie, placing another cookie on top, and freeze as described above.
Enjoy ice cream sandwiches right away or wrap the individual sandwiches in plastic wrap and place inside an airtight freezer storage bag or other freezer-safe container. Freeze until ready to enjoy, then transfer to refrigerator 10 to 15 minutes before serving. See Notes below.
Oil-free vegan cookies work well for ice cream sandwiches because they're still somewhat soft and chewy after cooling. Be careful not to overbake the cookies.
Once the ice cream sandwiches have been frozen for an extended period, say 4+ hours, the ice cream will be quite hard. Transfer individual sammies to the fridge 10 to 15 minutes before you plan to eat!
Store individually wrapped ice cream sandwiches in the freezer for up to a week for banana nice cream varieties and up to 2 weeks for higher fat ice creams.