Pour the milk into a medium saucepan, heat then place over medium heat and bring to a boil. Immediately turn off the heat and set it aside.
In a large bowl, whisk the egg yolks and sugar until light and thickened.
Sift in the cornstarch and whisk vigorously until no lumps remain.
Whisk in 1/4 cup of the hot milk mixture until incorporated.
Whisk in the remaining hot milk mixture, reserving the pot for later.
Pour the mixture through a strainer back into the pot.
Cook over medium-high heat, whisking constantly, until thickened and slowly boiling.
Cook while whisking for an additional minute or two after thickened and boiling.
Remove from the heat and stir in the butter.
Let cool slightly then cover with plastic wrap, lightly pressing the plastic against the surface to prevent skin from forming.
Chill in the refrigerator.
Cake:
Preheat oven to 350F.
Spray an 8-inch round cake pan with baking spray or butter and flour it. Line the bottom with parchment paper and spray again.
Combine flour, baking powder, and salt in a bowl, then whisk together and set aside.
In a stand mixer fitted with a whisk attachment or large mixing bowl if using a hand mixer, add eggs and sugar. Beat on medium speed until pale, thick, and fluffy, about 4 minutes. (Beater should leave a trail in eggs when lifted.)
Meanwhile, in a glass measuring cup, combine milk and butter. Microwave on high in 30-second intervals until butter is melted and milk is steaming.
With the mixer on low speed, gradually add the flour mixture to the egg mixture, beating just until combined.
Stir vanilla into the hot milk mixture. Slowly pour the hot milk mixture into the egg mixture beating until fully combined. (Batter will look like thick pancake batter and have bubbles on top.)
Scrape the sides of the bowl and fold the batter a few times to ensure it’s fully combined. Pour batter into the prepared cake pan.
Bake until a toothpick inserted in the center comes out clean and the cake begins pulling away from the sides of the pan, about 33 minutes.
Let cool in pan for a few minutes then invert onto a wire rack to cool completely.
Assembly:
Cut the cake in half horizontally.
Place the bottom half, cut side up on a serving plate.
Spread the chilled, thickened pastry cream over the cake, leaving a 1-inch border.
Top with the remaining cake half and gently press down to spread the filling to the edge.
Place in fridge and chill for at least 2 hours or overnight; cover with plastic or a cloche if chilling for more than two hours.
When ready to serve top with chocolate ganache.
Notes & Tips
Use a serrated knife to cut the cake in half. If you’re worried about cutting it evenly, place toothpicks a few inches apart around the equator. Use them as a guide for your knife. It’s also okay if it’s not perfect! It will taste great either way.
Use room-temperature eggs for the pastry cream and sponge cake. This will help the cream cook faster and the cake to whip up better for a fluffier texture.