Preheat the oven to 350°F. Lightly butter a 9x13-inch baking pan.

Sift together flour, baking powder and salt into a large bowl; set aside.

Combine egg yolks and 3/4 cup of the sugar in a large bowl and beat with an electric mixer on medium speed until pale yellow and airy, about 2 minutes.

Add whole milk and 1 1/2 teaspoons of the vanilla and beat until combined, scraping the sides of the bowl if needed.

Fold in flour mixture in three parts, stirring well after each addition; set batter aside.

In a second large bowl, beat egg whites on medium-high speed until soft peaks form.

Add remaining 1/4 cup sugar in two parts and beat until stiff peaks form.

Carefully fold egg white mixture into reserved batter in three parts, folding just until combined.

Gently transfer batter to the prepared pan and spread evenly with a spatula.

Bake about 20 minutes, or until cake is puffed and golden and a toothpick inserted into center comes out clean.

Cool cake completely in the pan on a wire rack. (Cake will shrink away from the sides of the pan as it cools.)

In a medium bowl, whisk together condensed milk, evaporated milk and remaining 1 1/2 teaspoons vanilla.

Pierce cooled cake all over with a fork or toothpick, then slowly pour milk mixture all over cake allowing it to soak in evenly.

Cover and refrigerate for at least 4 hours or overnight.

To serve, cut cake into squares and transfer to plates.