For the cream filling: Set a fine mesh strainer over a large measuring cup or bowl.

In a medium saucepan, whisk the whole milk, heavy cream, and ⅓ cup of sugar. In a medium bowl, whisk the egg yolks, cornstarch, salt, and the remaining ⅓ cup of sugar until smooth and lemon-yellow.

Heat the milk mixture over medium heat until steaming; remove from the heat. Remove 1 cup of the milk mixture and slowly drizzle it into the egg yolks while whisking constantly. Transfer the yolk mixture back to the pot and whisk to combine. Return to medium heat. Bring to a simmer and cook for 2 to 3 minutes, whisking constantly, until it thickens and bubbles. Then, remove it from the heat.

Press the mixture through the fine mesh strainer. Add the butter and vanilla to the mixture and stir until everything is combined. Press plastic wrap onto the surface (to prevent a film from forming). Let cool slightly, about 15 minutes. Chill in the refrigerator for at least 2 hours or overnight.

For the cake: Preheat the oven to 350°F. Spray 2, 9-inch cake pans with baking spray with flour. Line the bottoms with parchment paper and spray again.

In a medium bowl, combine the flour, baking powder, and salt.

In a glass measuring cup or microwave safe bowl, combine the milk and butter. Microwave the mixture in 15-second intervals until the butter is melted and the mixture is steaming.

In a large bowl, combine the eggs and sugar. With a hand mixer fitted with the whisk attachment, beat on high speed until pale and fluffy, about 5 minutes. Beat in the vanilla just until combined.

Whisk the hot milk mixture into the egg mixture by hand until incorporated. Add the flour mixture, mixing just until combined.

Divide the batter evenly into the prepared pans and bake for 22 to 27 minutes, or until a wooden pick inserted near the center comes out clean. Cool in the pans for 10 minutes. Run a butter knife around the sides of the pan and turn the cakes out onto a cooling rack. Remove the parchment paper. Let cool completely, about 1 hour.

Place one cake layer on a plate. Whisk the cream filling until smooth and spoon onto the cake, smoothing into an even layer about ½-inch from the edge of cake. Top with the remaining cake layer, placing the bottom side facing up. Place the cake in the refrigerator while preparing the ganache.

For the ganache: Place the chocolate chips, heavy cream, and oil in a glass measuring cup. Microwave the mixture at 50% power in 15-second intervals until the chocolate is melted, about 1 minute.

Pour the ganache over the center of the cake. Using an offset spatula, spread the ganache to the edges, allowing it to drip down the sides.

Chill the cake for at least 2 hours before slicing. Slice and serve, or wrap tightly and refrigerate for up to 1 day before serving.