Pour water to depth of 1 inch into bottom of a double boiler over medium heat; bring to a boil. Reduce heat to low, and simmer; place chocolate and 1/4 cup milk in top of double boiler over simmering water. Cook, stirring occasionally, 8 to 10 minutes or until melted. Remove from heat, and cool 10 minutes.
Meanwhile, cook remaining 3 cups milk and 1/4 cup sugar in a heavy non-aluminum saucepan over medium heat, stirring often, 8 minutes or just until it begins to steam (do not boil); remove from heat.
Whisk together eggs and remaining 1/4 cup sugar in a large bowl. Gradually whisk 1 cup hot milk mixture into egg mixture; gradually whisk egg mixture into remaining hot milk mixture.
Cook over medium heat, stirring constantly, 2 to 3 minutes. (A candy thermometer should register 160° or higher.) Stir in vanilla.
Remove from heat, and pour mixture through a non-aluminum fine wire-mesh strainer into a bowl. Whisk in melted chocolate mixture. Cover and chill 2 hours or until cold.
Pour mixture into freezer container of a 1-gal. electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and times will vary.) Serve with Raspberry Sauce or Quick Chocolate Sauce.
Note: We tested with Ghirardelli White Chocolate Baking Bar.