Nonstick baking spray
1 cup all-purpose flour
1 1/2 tsp. baking powder
1/4 tsp. salt
5 eggs
1 cup sugar, divided
1/3 cup milk
1 tsp. vanilla
1 can sweetened condensed milk
1 can evaporated milk
1/4 cup heavy cream
1 pt. heavy cream, for whipping (2 cups)
3 Tbsp. sugar
For the cake: Preheat the oven to 350°F. Spray a 13-by-9-inch pan liberally with baking spray until coated.
In a large bowl, combine the flour, baking powder, and salt. Separate the eggs.
Beat the egg yolks with 3/4 cup sugar on high speed until the yolks are pale yellow. Stir in the milk and vanilla. Pour the egg yolk mixture over the flour mixture and stir very gently until combined.
Beat the egg whites on high speed until soft peaks form. With the mixer on, pour in the remaining 1/4 cup sugar and beat until the egg whites are stiff but not dry.
Fold the egg white mixture into the batter very gently until just combined. Pour into the prepared pan and spread to even out the surface.
Bake until a toothpick comes out clean, about 30 minutes. Allow to cool.
In a small pitcher, combine the condensed milk, evaporated milk, and heavy cream. When the cake is cool, pierce the surface with a fork several times. Slowly drizzle all but about 1 cup of the milk mixture—try to get as much around the edges of the cake as you can. Allow the cake to absorb the milk mixture for 30 minutes.
For the icing: Whip the heavy cream with the sugar until thick and spreadable.
Spread over the surface of the cake. Cut into squares, and serve, or refigerate.