Make the Cake: Preheat the oven to 350 degrees F. Grease a 9x13-inch baking pan; set aside.
In a medium bowl, whisk together the cake flour, baking powder and salt; set aside.
Beat the butter with an electric mixer on medium speed until fluffy, about 1 minute. Decrease the speed to low and with the mixer still running, gradually add the sugar over 1 minute. Stop to scrape down the sides of the bowl, if necessary. Add the eggs, 1 at a time, and mix to thoroughly combine. Add the vanilla extract and mix to combine. Add the flour mixture to the batter in 3 batches and mix just until combined. Transfer the batter to the prepared pan and spread into an even layer. (This will appear to be a very small amount of batter.)
Bake for 20 to 25 minutes, or until the cake is lightly golden and reaches an internal temperature of 200 degrees F. Remove the cake to a cooling rack and allow to cool for 30 minutes. Poke the top of the cake all over with a skewer or fork. Allow the cake to cool completely and then prepare the glaze.
Make the Three-Milk Glaze: In a 4-cup measuring cup, whisk together the evaporated milk, sweetened condensed milk and the half-and-half. Once combined, slowly pour the glaze evenly over the cake. Refrigerate the cake for at least four hours, or overnight.
Make the Whipped Cream: Using an electric mixer, whisk together the heavy cream, sugar and vanilla on low speed until stiff peaks form. Increase to medium speed and whip until thick. Spread the topping over the cake and allow to chill in the refrigerator until ready to serve. Leftover cake should be covered and refrigerated for up to 1 day.