Set a large fine strainer over a medium bowl and set the bowl in a shallow pan of cold water.

In a large saucepan, combine the half-and-half and vanilla bean and cook over moderately low heat just until small bubbles appear around the rim, about 5 minutes.

In another medium bowl, whisk the sugar and egg yolks just until combined. Whisk in half of the hot half-and-half in a thin stream. Pour the mixture into the saucepan and cook over moderate heat, stirring constantly with a wooden spoon, until the sauce has thickened slightly, 4 to 5 minutes. Immediately strain the sauce into the bowl in the cold water bath to stop the cooking. Scrape the vanilla seeds into the sauce. Serve right away or refrigerate until chilled.