Preheat the oven to 350°F (175°C). Line the bottom of a 9×13-inch baking pan with parchment; do not grease the sides.
In a bowl, whisk together the all-purpose flour, baking powder, and fine salt until evenly combined.
Place the 5 separated egg yolks in a large bowl. Add 0.75 cup of the granulated sugar and beat with a mixer on high until thick and pale, 2–3 minutes. Mix in 1 tsp of the vanilla extract and 0.33 cup of the whole milk.
In a clean bowl, beat the 5 egg whites on medium speed to soft peaks, 1–2 minutes. Gradually add the remaining 0.25 cup granulated sugar and continue beating to glossy medium-stiff peaks, 1–2 minutes more.
Fold one-third of the whipped whites into the yolk mixture to lighten. Sprinkle the flour mixture over the batter and fold in gently, alternating with the remaining whites in 2 additions, just until no dry streaks remain. Spread the batter evenly in the pan.
Bake until the top is golden, the cake springs back to a light touch, and a toothpick comes out clean, 25–30 minutes. Cool in the pan on a rack for 30 minutes.
Using a skewer or fork, poke holes all over the cake, going nearly to the bottom but not tearing the surface.
For the milk soak, whisk together the evaporated milk, the sweetened condensed milk, 1 cup of the remaining whole milk (reserve was from the total measured), and 1 tsp vanilla extract until smooth.
Slowly ladle or pour the milk mixture evenly over the cake, allowing it to seep in. Let stand at room temperature 20–30 minutes until most of the liquid is absorbed, then cover and refrigerate at least 3 hours or up to overnight.
For the topping, whip the heavy cream with the powdered sugar and the remaining 1 tsp vanilla extract to medium-soft peaks, 2–4 minutes. Spread evenly over the chilled cake.
Dust the top lightly with ground cinnamon, slice into 12 squares, and serve chilled.