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Put milk in 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.