In a large saucepan, combine milk, sugar, and egg yolks.
Cook and stir over medium heat just until mixture coats a metal spoon.
Remove from heat.
Add melted chocolate, beating with a wire whisk until smooth.
Cover surface of chocolate mixture in saucepan with plastic wrap.
Chill for several hours or overnight until very cold. (Or quickly chill mixture by transferring it to a large bowl. Place bowl in sink of ice water for 30 to 60 minutes, stirring occasionally.)
Pour chocolate mixture into freezer canister of 4 or 5 quart ice cream freezer.
Freeze according to manufacturer's directions.
If desired, stir chopped chocolate into gelato and ripen about 4 hours.
If desired, sprinkle each serving with additional shaved chocolate.