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Step 1
Heat oven to 350 degrees. 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.
Step 2
In a medium bowl, whisk together the flour, baking powder and salt. In a large bowl, with an electric mixer on medium-high, beat the egg yolks and 1/2 cup/100 grams 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.
Step 3
In another large bowl, with clean beaters, whip the egg whites until foamy and the yellowish color has disappeared, about 1 minute. Slowly add the remaining 1/2 cup plus 2 tablespoons/125 grams 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 spatula, gently fold the remaining whites into the batter without deflating them.
Step 4
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.
Step 5
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).
Step 6
To serve, whip the cream and confectioners’ sugar to soft peaks. Top the cake with the whipped cream.