Prepare the Cookie Cups:

1. Preheat the Oven: Preheat your oven to 350°F (175°C). Lightly grease a 12-cup muffin tin.
2. Mix the Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
3. Cream the Butter and Sugars: In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.
4. Add the Egg and Vanilla: Mix in the egg and vanilla extract until smooth and well combined.
5. Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet mixture, stirring just until combined. Do not overmix.
6. Shape the Dough: Divide the dough into 12 equal portions. Roll each portion into a ball and press it into the muffin tin to form a cup shape, pressing it up the sides to create space for the custard filling.
7. Bake: Bake in the preheated oven for 12-15 minutes, or until the edges are golden brown. Allow the cookie cups to cool in the tin for 5 minutes, then carefully transfer them to a wire rack to cool completely.

Prepare the Vanilla Custard Filling:

8. Heat the Milk: In a small saucepan, heat the milk over medium heat until it’s just about to simmer (do not boil).
9. Whisk the Egg Yolks and Sugar: In a separate bowl, whisk together the egg yolks, sugar, and cornstarch until smooth and pale.
10. Temper the Egg Mixture: Slowly add the hot milk to the egg mixture, whisking constantly to prevent curdling.
11. Cook the Custard: Return the mixture to the saucepan and cook over medium heat, stirring constantly, until the custard thickens and coats the back of a spoon, about 5-7 minutes.
12. Add Vanilla and Butter: Remove from heat and stir in the vanilla extract and butter until smooth. Let the custard cool slightly.

Assemble the Cookie Cups:

13. Fill the Cookie Cups: Once the cookie cups and custard have cooled, spoon the custard into each cookie cup, filling them to the brim.
14. Chill: Place the filled cookie cups in the refrigerator for at least 30 minutes to allow the custard to set.