Place as many frozen bananas into a high-speed blender or food processor. Add the peeled mandarins. A good ratio to start with is 1 mandarin for every 1 frozen banana used.
For every 1 banana used, throw in a small knob, or about a 1/4" thick slice of fresh ginger. If you know you love that ginger kick, feel free to add extra.
Blend on high until all is well blended and smooth, about one minute. Add in minimal amounts of water if needed to help blend.
I love eating straight out of the blender as a soft-serve, but if you want more of a firm ice cream consistency, scoop into a container, cover, and let set up in the freezer.