Stir together milk, sugar, vanilla bean and seeds in a large heavy saucepan over medium heat. Bring to a simmer, stirring regularly until sugar is completely dissolved.
Add baking soda and stir to combine. Reduce heat to low and cook at a very mild simmer for 1 hour, stirring occasionally.
Remove vanilla bean, then continue to cook at a low simmer until mixture has caramelized and is dark brown in color and reduced to about a cup of dulce de leche, another 1 1/2 to 2 hours. Stir more frequently to avoid burning as milk caramelizes.
Strain through a sieve and store in the refrigerator for up to a month.