Whisk together first 5 ingredients in a heavy saucepan. Cook over medium-low heat, whisking constantly, 10 to 12 minutes or until mixture reaches a chilled pudding-like thickness.
Remove from heat; stir in bourbon and vanilla. Cool to room temperature (about 1 hour).
Place plastic wrap directly on mixture (to prevent a film from forming), and chill 6 to 24 hours.
