Combine the sugar, cornstarch and salt in a large saucepan. Whisk in the half-and-half and yolks.

Cook while stirring until the base thickens and coats a spoon. Remove from the heat, then stir in the cream and vanilla.

Refrigerate the base for several hours or overnight. It must be cold before churning.

Put the chilled base in the specified large ice cream freezer. Add milk to its 4-quart fill mark, leaving the expansion space required by the manufacturer.

Churn until thickened, then stir in the chopped candy and optional cherries.

For an ice-and-salt freezer, replenish the ice and salt as directed and allow about 2 hours for hardening. Follow the machine's capacity and operating instructions.