Peel bananas and slice into 1/2 inch pieces. Slice the strawberries. Arrange banana slices and strawberry slices in a single layer on a large plate or baking sheet. Freeze for 2 hours or overnight.
Place the frozen banana slices and strawberry slices in a food processor or powerful blender. Puree mixture, scraping down the bowl as needed. Puree until the mixture is creamy and smooth. This will take awhile. Don't worry, the bananas and strawberries will come together. Keep scraping and mixing!
Serve immediately for soft-serve ice cream consistency. If you prefer harder ice cream, place in a freezer container and freeze. When ready to serve, let the ice cream sit out for 5 minutes. It will be hard right from the freezer, but it will soften up and you will be able to scoop it.
*Note-Make sure you use a powerful food processor or blender!