Beat softened butter and sugar until light and fluffy.
Add egg and vanilla extract, mixing until combined.
Whisk flour, baking powder, and salt in a separate bowl.
Gradually mix dry ingredients into wet ingredients until just combined.
Chill dough for at least 30 minutes.
Preheat oven to 350°F (175°C).
Scoop rounded tablespoons of dough onto parchment-lined baking sheets.
Bake cookies for 10 to 12 minutes until edges are lightly golden.
Cool cookies completely on a wire rack.
Whisk egg yolks, sugar, and cornstarch in a bowl for the pastry cream.
Heat milk to simmering, then gradually whisk hot milk into yolk mixture.
Return mixture to saucepan and cook over medium heat, whisking constantly until thickened.
Remove from heat, stir in vanilla, cover surface with plastic wrap, and chill thoroughly.
Heat heavy cream until simmering; pour over chocolate chips and let sit for 5 minutes.
Whisk chocolate and cream until smooth and let cool to spreadable consistency.
Slice cooled cookies horizontally and spread pastry cream on bottom halves.
Top with other cookie halves and dip or drizzle tops with chocolate ganache.
Allow ganache to set before serving.