Combine the milk, sugar, vanilla bean and seeds in a large, 4-quart saucepan and place over medium heat. Bring to a simmer, stirring occasionally, until the sugar has dissolved.
Once the sugar has dissolved, add the baking soda and stir to combine. Reduce the heat to low and cook, uncovered, at a bare simmer. Stir occasionally, but do not re-incorporate the foam that appears on the top of the mixture. Continue to cook for 1 hour.
Remove the vanilla bean after 1 hour and continue to cook until the mixture is a dark caramel color and has reduced to about 1 cup, 1 1/2 to 2 hours. Strain the mixture through a fine-mesh strainer. Store in the refrigerator in a sealed container for up to 1 month.