Slice the bananas before you freeze them. (Freeze the bananas in a single layer on a tray or plate lined with parchment or wax paper. Once the slices are frozen, use them immediately or keep frozen in a zip-top plastic bag or airtight container for up to a month.)
Freeze the berries whole.
Remove frozen fruit from the freezer and process or pulse the banana slices and berries in a food processor until the mixture is the texture of soft-serve ice cream, scraping down the sides as necessary. Don’t worry if the mixture is not totally smooth at first. Once the bananas start to break down and defrost in the food processor, they’ll give in and the “ice cream” will take shape quickly.