Prepare the pastry cream: Whisk milk and about half the sugar in a saucepan over medium heat until steamy (do not boil). In a bowl, whisk remaining sugar, cornstarch, and egg yolks until pale. Slowly temper the yolks by adding half the hot milk while whisking constantly. Return everything to the saucepan and whisk constantly over medium heat for 2-3 minutes until thick and boiling. Remove from heat and immediately whisk in butter and vanilla. Cool in a bowl with plastic wrap pressed directly on the surface for at least 2 hours.

Make the cookies: Cream butter and sugar until light and fluffy. Mix in eggs, vanilla, and milk. Gradally add dry ingredients (flour, baking powder, salt) until just combined. Chill dough 30 minutes if needed.

Bake: Preheat oven to 350°F (175°C). Scoop 1.5-tablespoon mounds 2 inches apart onto parchment-lined baking sheets. Bake 9-11 minutes until edges are set but centers are soft. Cool on the pan for 5 minutes, then on a wire rack completely.

Whip Ganache: Place chocolate chips in a bowl. Heat heavy cream and corn syrup until simmering (do not boil). Pour over chocolate and let sit 5 minutes. Gently whisk until smooth. Cool and thicken slightly if needed.

Assemble: Ensure all components are completely cool. Place about 1.5 tablespoons of pastry cream on the flat side of half the cookies, topping with remaining cookies. Spoon the chocolate ganache glaze generously over the top of each sandwich. Let set for 15 minutes before serving.