Bring milk, sugar, and vanilla extract to a boil in a saucepan over high heat. Reduce heat to medium-low, continue cooking, and continuously stirring until milk has thickened and turned a caramel color, about 1 hour or more.

Stir in baking soda. Continue cooking until caramelized milk has reached a pudding consistency. Pour manjar into a bowl and cool completely in the refrigerator.