Line a baking sheet or plate with parchment paper.
Slice bananas into 1/2-inch rounds and arrange them in a single layer on the prepared sheet so pieces are not touching.
Freeze the banana slices until firm, about a few hours up to overnight (do not freeze longer than 24 hours to avoid browning).
Remove the frozen slices from the sheet and transfer them to a resealable freezer bag; squeeze out excess air and return to the freezer until ready to use.
When ready to make soft serve, fit the food processor with the blade and add the frozen banana pieces.
Pulse a few times to break the pieces into crumbs, then process continuously, stopping occasionally to scrape and redistribute the mixture with a spatula so it processes evenly.
Continue processing until the bananas become smooth and creamy with the consistency of soft-serve ice cream.
Scoop the soft serve into bowls and serve immediately, or transfer to a container and freeze briefly if you prefer a firmer texture.