Combine milk and sugar in a tall, heavy-bottomed sauce pan. Bring to a simmer over medium heat, stirring often. Remove from the heat and carefully stir in the baking soda – the mixture will bubble and foam up. Add the vanilla bean and return to the heat.

Cook, stirring every 10 minutes, until the mixture has reduced to a thick but pourable sauce (it will look like a vat of bubbling tar at this point), about 50 to 60 minutes. Reduce the heat slightly and stir every 5 minutes for another 20 to 30 minutes, until the sauce is very thick. To check consistency, drop 1/4 teaspoon into a glass of ice water – it should seize into a soft droplet (soft ball).

Strain the mixture into a metal bowl, removing the vanilla pieces, and allow to cool completely before using.

This recipe can easily be doubled, but the cooking time will be longer. Store sauce covered and refrigerated for up to one month.