Whisk together the first 3 ingredients in a large heavy saucepan. Gradually whisk in the milk and half-and-half. Cook over medium heat, stirring constantly, 10 to 12 minutes or until the mixture thickens slightly. Do not simmer. Remove from the heat.
Whisk the egg yolks together until slightly thickened in a medium mixing bowl. Gradually whisk about 1 cup of the hot milk mixture into the yolks, then pour them into the remaining hot mixture, whisking constantly. Scrape seeds from vanilla bean into the hot mixture. Allow to cool 30 minutes, stirring occasionally.
Place plastic wrap directly on the surface of the custard (to prevent a film from forming), and chill 8 to 24 hours.
Pour the custard into the freezer container of a 1 1/2-quart electric ice-cream maker, and freeze according to the manufacturer’s instructions.