Making the Custard Filling:
Heat the milk: In a medium saucepan, heat the milk over medium heat until it starts to simmer.
Mix the egg yolks and cornstarch: In a separate bowl, whisk together the egg yolks, sugar, and cornstarch until smooth and pale.
Temper the eggs: Slowly pour the hot milk into the egg mixture, whisking constantly to prevent the eggs from scrambling.
Cook the custard: Return the mixture to the saucepan and cook over medium heat, stirring constantly, until it thickens and comes to a boil.
Add vanilla and butter: Remove from heat, stir in the vanilla extract and butter until smooth. Transfer the custard to a bowl, cover with plastic wrap (pressing it directly onto the surface to prevent a skin from forming), and refrigerate until completely cool.
Making the Cookie Base:
Cream the butter and sugars: In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Beat until light and fluffy.
Add the egg and vanilla: Mix in the egg and vanilla extract until well combined.
Combine the dry ingredients: In a separate bowl, whisk together the flour, baking soda, and salt.
Mix the dough: Gradually add the dry ingredients to the wet mixture, stirring just until combined.
Assembly and Cooking
Preparing the Cookie Cups:
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