In a large saucepan or pot*, combine the milk, sugar, and vanilla. Stir to combine. Heat over medium heat until the sugar has dissolved and the mixture is simmering.
Add the baking soda and stir to combine. When the baking soda is added, a lot of foam will be produced. If it looks like it will overflow, remove from heat immediately and continue stirring until the foam subsides. Return to low heat and allow to simmer for 2 1/2 to 3 hours, stirring every 20 to 30 minutes. As foam forms on the surface, skim it off. Do not mix it back into the mixture.
*Use a larger saucepan or pot than you think you'll need!