Prepare Custard Ahead:
Vigorously whisk together egg yolks and sugar until completely combined and lightened. Add flour and cornstarch, whisk very well and set aside.
Heat milk, heavy cream, butter, and salt until simmering.
Slowly add the heated milk mixture into the egg yolk mixture, stirring constantly. Whisk well.
Return the mixture to the pot and bring to a simmer, stirring constantly until it thickens. Do not walk away.
Remove from heat and whisk in the vanilla extract.
Transfer custard into a container, cover with plastic wrap or a lid, and refrigerate for at least two hours or overnight.
Cake:
Preheat Oven:
Preheat oven to 375°F (190°C). Line a 17x11x1-inch pan with parchment paper and spray with cooking oil spray, including the sides.
Prepare Cake Batter:
Beat eggs with an electric mixer on high speed for 5 minutes until thick and light yellow.
Slowly beat in granulated sugar.
Lower speed to low and add water and vanilla extract.
Slowly add flour, baking powder, and salt. Beat just until batter is smooth. Scrape sides and bottom of the bowl and mix just until combined.
Bake Cake:
Pour batter into prepared pan and spread evenly.
Bake for 8 minutes or until the center of the cake is done.
Run a spatula around the edges of the pan to loosen the cake. Let it rest for a couple of minutes.