In a medium saucepan, combine 2 2/3 cups milk, the sugar and salt. Scrape in the vanilla bean seeds and add the vanilla pod. Bring to a simmer over medium heat and cook, stirring occasionally, until the sugar dissolves, 7 to 9 minutes.
Remove the vanilla bean, slowly whisk in the farina and cook for 2 minutes , whisking constantly. Remove from the heat and briskly whisk in the eggs. Return to the heat and cook, whisking, for 1 minute. Whisk in the butter until melted. Stir in the remaining 1/3 cup milk. Serve warm or at room temperature.