Heat oven to 375°F. Butter 9”x13” baking pan. Dust pan with flour, tapping out excess; set aside. In a medium bowl, whisk together 2 cups flour and baking powder; set aside.
Crack 6 egg whites into a large bowl; reserve yolks. Using an electric mixer, beat egg whites until frothy. Gradually add 1 cup sugar and continue beating until stiff peaks form, about 5 minutes. Add 6 egg yolks, one at a time, mixing until incorporated. Alternately beat in flour mixture and milk to egg mixture, starting and ending with flour mixture. Stir in vanilla. Pour cake batter into prepared pan. Bake until toothpick inserted in center comes out clean, 30 – 35 minutes. Let cool 10 minutes and poke holes into cake using a 2-pronged meat fork.
Meanwhile, pour condensed milk, evaporated milk and heavy cream into a bowl. Transfer half of the liquid to a small saucepan. Bring milk mixture to a boil; remove from heat and stir in remaining mixture. Pour milk slowly over cake until absorbed; cover and transfer to the refrigerator; chill 1 hour.
Meanwhile, in bowl of double boiler, using a whisk, beat 3 egg whites until frothy. Gradually add remaining sugar. Continue beating until stiff-peaks form and meringue is shiny, about 5 minutes. Whisk in lime juice. Spread meringue over top of cake. Store leftovers (if any) in refrigerator.
In this recipe, to be sure the egg whites have reached the “stiff peak” stage, simply lift the hand mixer out of the egg whites. If the egg whites stand up straight without flopping over, they are done. For extra assurance, scoop out a spoonful of the egg white mixture and hold the spoon upside down. If the whites stay put, they’re ready!