Ice Cream
3 cups whipping cream
1 cup whole milk
1 vanilla bean, split lengthwise
6 large egg yolks
1 cup granulated sugar
1/4 cup dark rum
1/4 teaspoon ground nutmeg

Combine whipping cream and milk in heavy medium saucepan. Scrape in seeds from vanilla bean. Add bean. Bring to simmer. Whisk egg yolks and sugar in large bowl to blend. Gradually whisk in hot cream mixture. Return mixture to saucepan. Stir constantly over medium-low heat until custard thickens and leaves path on back of spoon when finger is drawn across, about 5 minutes (do not boil). Strain into large bowl. Mix in rum and nutmeg. Refrigerate until cold.

Process mixture in ice cream maker according to manufacturer's instructions. Transfer to container and freeze. Can be made 4 days ahead. Keep frozen.

Sauce
6 tablespoons unsalted butter
1 cup packed golden brown sugar
1/3 cup whipping cream
2 tablespoons light corn syrup
2 tablespoons dark rum

Melt butter in heavy medium saucepan over medium heat. Add brown sugar, cream and corn syrup. Boil 1 minute. Remove from heat. Mix in rum. Cool slightly. (Can be made 1 day ahead. Cover and refrigerate. Rewarm before using.)

Scoop ice cream into bowls. Spoon warm sauce over ice cream.