Peel bananas and cut into approximately ½-inch slices. Place in an airtight container with the strawberries and freeze for several hours, until frozen solid, or preferably overnight.
In a food processor (see note), combine the frozen bananas and strawberries with 2 tablespoons nondairy milk or coconut creamer. Add a pinch of cinnamon if using.
Process until the bananas and strawberries are broken down to bits, then stop the machine to scrape down.
Process again until the mixture is completely smooth and creamy, adding a bit more of the nondairy milk or creamer if the mixture needs it to become smooth.
Scrape the banana ice cream into a container and refreeze for an hour or two, or until firm enough to scoop. Or if you want to serve right away as soft serve, spoon into bowls or cones (or in adorable waffle bowls as shown in the photos).