In a mixing bowl, whisk together the egg yolks, condensed milk, and evaporated milk until smooth and well combined.

Strain the mixture through a fine-mesh sieve to remove any lumps and ensure a silky texture.

Pour the strained mixture into a saucepan and heat over low to medium heat, stirring continuously to prevent curdling.

Bring to a gentle simmer, then turn off the heat.

Add the vanilla extract and mix well to enhance the flavor.

Allow the custard milk to cool completely before using.

Set aside until ready to serve.