Combine first three ingredients in a heavy saucepan over medium-high heat. Scrape seeds from vanilla bean; add seeds and bean to milk mixture. Heat to 180 or until tiny bubbles form around edge (do not boil).
Combine sugar, bourbon, nutmeg and egg yolks in a bowl, stirring with a whisk. Gradually add half of hot milk mixture, whisking constantly. Return milk mixture to pan. Reduce heat to medium. Heat to 160, stirring constantly. Discard vanilla bean and cinnamon stick. Pour mixture into a bowl, and place plastic wrap on surface of custard. Chill thoroughly.
Process in ice cream maker according to manufacturer's instructions. Transfer to a freezer-safe container, cover and freeze for 8 hours or until firm.