Preheat the oven to 350 degrees F (175 degrees C). Grease and flour an 8x12-inch baking dish.
Separate 5 eggs. Beat egg whites in a large bowl. Add 1 cup sugar slowly to egg whites, beating constantly. Add yolks one at a time, beating well after each addition. Stir in 1 teaspoon vanilla. Sift flour over egg mixture and stir until well combined. Pour batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 minutess. Allow to cool completely.
Blend together sweetened condensed milk, evaporated milk, milk, and 1 tablespoon vanilla. Pour over cooled cake.
Beat 3 egg whites in a clean mixing bowl to soft peaks. Gradually add remaining 1 cup sugar and continue beating until stiff meringue forms. Stir in remaining 1 teaspoon vanilla.