Blend the custard, cream, bananas, half the strawberries and the maple syrup together in a blender or food processor until smooth.
Pour the mixture into a freezer-proof container and freeze for 3 hours until just starting to freeze around the edges.
Scrape the mixture into a bowl and beat with a stick blender until smooth. Finely chop the remaining strawberries, stir into the mixture and pour back into the freezer-proof container. Freeze for 3–4 hours or overnight until firm. Allow to soften for 15 minutes before serving.