Cut cherimoya lengthwise into 8 wedges.
Trim off and discard peel; scoop out seeds.
Chop enough fruit to make about 1 1/4 cups.
In a 1- to 2-quart pan, combine sugar and water.
Bring to a boil over high heat; cook until mixture is reduced to 1/2 cup (about 5 minutes).
Let cool completely.
In a blender or food processor, combine cherimoya and orange juice; whirl until pureed.
Pour mixture into a 9-inch square baking pan; cover and freeze until firm (about 1 hour).
Breakfruit into small chunks.
In a food processor or with an electric mixer, beat just until mixture forms a smooth slush.
Wrap airtight and freeze until firm (at least 2 hours).
Or freeze mixture in an ice cream freezer, following manufacturer's directions, until firm.
If made ahead, freeze for up to 1 month.