Peel and cut the banana into large chunks. Freeze on a parchment-lined baking sheet until frozen.

When the banana is frozen, add it to the bowl of a food processor with the lime juice and milk. Pulse 2-3 times to incorporate and then process on low speed until it becomes smooth (about 20-40 seconds). Do not over-process it because we want it to stay as cold as possible and overusing the blades can quickly heat up the mixture.

Add the strawberries and shredded coconut. Pulse 4-5 times until incorporated and slightly broken down.