Prepare for Baking - Heat oven to 350°F (177°C). Butter the bottom of a 13-by-9-inch pan lightly, leaving a 1/4-inch border that remains ungreased. Do not butter the sides of the pan; you want the cake to “climb” up the sides of the pan as it bakes.
Make Cake Batter - In a medium bowl, whisk together the flour, baking powder and salt. In the bowl of a stand mixer, beat the egg yolks and 1/2 cup of the sugar until pale and thick, about 3 minutes. Beat in 1/2 cup of the milk, lower the speed, and then mix in the flour mixture just until combined. Scape everything back into the big bowl and rinse out the mixer bowl. With whisk attachment, whip the egg whites until foamy about 1 minute. Slowly add the remaining 1/2 cup plus 2 tablespoons sugar while beating. Continue to beat the mixture until you have shiny, medium-stiff peaks, about 2 minutes. Stir a big scoop of the egg white mixture into the batter to loosen it, then, using a rubber spatula, gently fold the remaining whites into the batter without deflating them.
Bake Cake - Pour the batter into the prepared pan and smooth the top. Bake until golden brown and a toothpick inserted into the center comes out clean, 25 to 30 minutes. Transfer cake to a rack to cool slightly.
Infuse Cake with Milks - Meanwhile, in a medium bowl, whisk together the remaining 1 cup milk, condensed milk, evaporated milk and vanilla. Using a skewer or a toothpick, poke holes about 1/2 inch apart all over the cake. Cut the edges of the cake from the sides of the pan. Pour the milk mixture evenly over the cake, about a cup at a time, allowing 5 to 10 minutes for it to soak in before adding more. Cover and refrigerate for at least 2 hours (or up to 24 hours).
Serve - To serve, whip the cream, vanilla extract and confectioners’ sugar to soft peaks. Top the cake with the whipped cream. Serve.