Put milk into a large, deep, heavy saucepan over medium-high heat. Bring to a
boil and allow skin to form on top of milk. Do not stir. Skin will thicken and puff
up; then reduce heat to medium and remove skin.
Increase heat to medium-high and
repeat process three more times. The skin will become thinner with each boil. Resist
the urge to stir milk.
Add sugar and vanilla bean after fourth and final boil, then stir until sugar
has melted, about 2 minutes.
Reduce heat to medium-low and stir in baking soda.
Simmer milk, stirring often, yet taking care not to disturb film of cooked milk
forming on the inside of the saucepan. Simmer, skimming foam while milk cooks, until
reduced by half, about 1 hour.
Reduce heat to low and simmer, skimming occasionally,
until milk is very thick and golden, about 3 1/2 hours more. Mixture will brown
as it cooks.
Strain cooked milk through a sieve into a bowl, then cover and refrigerate. Mixture
will thicken as it cools.
Serve with fruit, such as strawberries or bananas, or with toast, if you like.