In a large saucepan, add the milk, rice, salt, vanilla bean (if using, extract...don't add it yet.) and sugar over medium heat.

Bring the mixture to a boil, stirring frequently.

Reduce the heat to low and simmer, covered for 15 minutes stirring occasionally.

Uncover and continue to simmer until the rice is tender and the pudding has reduced to about 3 1/2 cups. Continue to stir constantly to prevent scorching.

Fish out the vanilla bean and scrape out the seeds.

Turn off the heat and stir in the butter, vanilla bean seeds or vanilla extract.

Transfer the pudding to a bowl and cover the surface with plastic wrap to prevent a skin from forming.

Chill for 1 hour or overnight.

Serve warm or chilled.