Preheat oven to 350Line a 9×13-inch pan with aluminum foil, spray with floured cooking spray or grease and flour the pan; set aside.
To the bowl of a stand mixer fitted with the paddle attachment (or a large bowl and handheld electric mixeadd the 5 egg yolks, 3/4 cup granulated sugar, and beat on medium-high speed until pale yellow and doubled in volume, about 4 minutes. Stop and scrape down the sides of the bowl.
Add 1/3 cup whole milk, vanilla, flour, baking powder, salt, and beat on low speed until combined, don’t over-mix; set aside.
To a medium bowl, add the egg whites and beat with a handheld electric mixer on high speed until soft peaks form. Gradually add remaining 1/4 cup sugar and continue beating until stiff peaks form but egg whites are not dry.
Gently fold egg whites into the cake batter.
Turn batter out into prepared pan, smoothing the top lightly with a spatula. Bake for about 32 to 35 minutes (I baked 33 minuteor until cake is set in the center, springy to the touch, and a toothpick inserted in the center comes out clean or with a few moist crumbs, but no batter.
Allow cake to cool in pan on a wire rack. While cake cools, make the tres leches mixture.