In a 2-quart heavy saucepan bring 2 cups of the milk, 2 tablespoons of the sugar, and the scraped vanilla bean to a boil over medium heat.
In a large bowl, whisk together the egg yolks and remaining 2 tablespoons of sugar. Slowly pour 1 cup of the hot milk mixture, whisking constantly, into the egg yolk-sugar mixture. (Do not pour the entire yolk-sugar mixture into the boiling milk mixture, as it will curdle the eggs.) Whisk in the remaining milk. Pour the milk-yolk mixture into the saucepan and cook over medium heat, stirring constantly, until the mixture coats the back of a spoon. Do not boil.
Remove from the heat and stir in the rum. Strain the mixture through a fine wire sieve into a heat--proof bowl. Place the sauce in an ice bath. When cool, transfer the sauce to a bowl. Cover the surface with plastic wrap and chill in the refrigerator, until ready to use. Sauce will keep in the refrigerator for 4 to 5 days if well sealed.