Combine sugar and cocoa in a medium, heavy saucepan over medium-low heat. Stir in 1/2 cup milk and egg yolks. Stir in remaining 2 cups milk. Cook 12 minutes or until a thermometer registers 160°, stirring constantly. Remove from heat.
Place half-and-half in a microwave-safe dish; microwave at high 1 1/2 minutes or until half-and-half boils. Add chocolate to half-and-half; stir until smooth. Add half-and-half mixture to pan; stir until smooth. Place pan in an ice-filled bowl. Cool completely, stirring occasionally.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container; cover and freeze 1 hour or until firm.