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