Preheat the oven to 350 °F (180 °C).
In a bowl, whisk together the flour, baking powder, and salt.
In another bowl, beat the softened butter and sugar until creamy.
Add the egg and vanilla extract to the butter mixture and combine.
Gradually add the dry ingredients to the wet ingredients and mix until just combined.
Press the dough evenly into the cups of a mini muffin tin to form small shells.
Bake for 10–12 minutes until the edges are lightly golden, then cool in the pan.
Heat the milk in a small saucepan until warm.
Whisk together sugar, cornstarch, and egg yolk in a bowl until smooth.
Slowly pour the warm milk into the egg mixture while whisking constantly.
Return the mixture to the saucepan and cook over medium heat, stirring continuously until thickened.
Remove from heat, stir in vanilla and butter, then let the filling cool.
Fill each cooled cookie cup with the vanilla filling by spooning or piping.
Melt chocolate chips with butter or cream until smooth.
Drizzle or spoon the melted chocolate over each filled cookie cup.
Allow the chocolate to set slightly, then serve at room temperature.