Preheat oven to 350. Spray a 13x9-inch baking dish liberally.
Combine flour, baking powder, and salt in a large bowl. Make sure you properly measure out your flour - don't pack it in the measuring cup like you would brown sugar! (That will kill this cake, and it'll come out too dense.) Separate your eggs.
Beat egg yolks with 3/4 cup of the sugar on high, until pale yellow. Stir in the milk and vanilla. Pour egg yolk mixture over the bowl of dry ingredients, and stir very gently until combined.
Grab a new mixing bowl (or quickly clean the one you just used) and whip your egg whites on high speed until soft peaks form. With the mixer on, pour in the remaining 1/4 cup of sugar. Beat until egg whites are stiff (but not dry).
Fold the egg white mixture into the batter very gently - just until combined. Pour into the prepared baking dish and spread to even out the surface. Bake for 35-45 minutes, or until a toothpick comes out clean. Cool completely.
While cake is cooling, combine the condensed milk, evaporated milk, and half & half in a pitcher or large measuring cup. When cake is cool, pierce the surface with a cake - you can't poke enough! Slowly drizzle all but about 1/2 cup of the milk mixture over the cake. (Don't forget the edges!)
Allow the cake to soak up the milks, about 30 minutes. To ice the cake, many people use Cool Whip. I prefer to make my own sweetened vanilla whipped cream, which is what is pictured. Serve and enjoy! (You'll have a second piece!)