Bring 2 1/4 cups milk just to a boil in a 4-quart heavy saucepan over moderate heat.
While milk is heating, whisk together sugar, cornstarch, salt, and 1/4 cup (cold) milk in a bowl until smooth, then whisk into boiling milk and bring to a boil over moderate heat, whisking.
Boil, whisking frequently, 3 minutes (mixture will be very thick).
Remove from heat.
Bring remaining 1/2 cup (cold) milk just to a boil in a 1-quart heavy saucepan over moderate heat.
Pour hot milk over chocolate in a bowl and let stand until chocolate is melted, about 1 minute, then whisk until smooth.
Stir into cornstarch-milk mixture and force through a fine-mesh sieve into a bowl.
Cool slightly, stirring frequently to prevent a skin from forming, then cover surface with wax paper and chill until cold, at least 1 1/2 hours.
Freeze mixture in ice cream maker, then transfer to an airtight container and freeze until hardened, about 3 hours.
Let soften 5 minutes before serving.