Bring 1 3/4 cups milk, 1/2 cup sugar, zest, and a pinch of salt to a simmer in a 2-quart heavy saucepan over moderate heat.
Whisk together cornstarch and remaining 1/4 cup milk in a small bowl until smooth, then whisk into simmering milk. Bring to a boil, whisking constantly, and boil 1 minute.
Transfer mixture to a metal bowl, then set bowl in a larger bowl of ice and cold water and cool completely, stirring frequently. Discard zest.
Quarter, pit, and peel avocados, then purée with vitamin C and remaining 1/4 cup sugar in a food processor until smooth.
Add milk mixture and blend well.
Freeze avocado mixture in ice cream maker.
Transfer to an airtight container and freeze until hardened, about 1 hour.
