Position rack in center of oven and preheat oven to 350°F.
In a medium bowl, whisk together the flour, cornstarch, baking powder and baking soda; set aside.
In a large bowl, use an electric mixer to beat the butter until creamy. Blend in the sugar and beat for a couple of minutes until light and fluffy, scraping bowl halfway through. Add eggs, mixing each one in until fully incorporated before adding the next. Stir in the vanilla. With the mixer on low, slowly blend in the flour mixture until fully combined, but do not over beat.
Spread batter into a 9- by 13-inch baking pan or dish (I used Pyrex) and bake for 25 to 30 minutes, until cake is golden brown and toothpick inserted in center comes out clean.
While the cake is baking, combine the half-and-half, sweetened condensed milk, and evaporated milk in a medium saucepan over medium heat on the stove. Heat, stirring occasionally, until warm and well-combined.
Once the cake is done, allow it to cool in the pan for 10 minutes before piercing the top all over with a wooden skewer. Slowly and evenly pour the warm milk mixture all over the top of the cake. Cover the cake tightly with plastic wrap and refrigerate overnight, up to 24 hours.
Before serving, make the topping by pouring the heavy whipping cream, vanilla, and powdered sugar into a bowl. Use an electric mixer on low to combine, then beat on medium-high to high speed until stiff peaks just form. Spread the whipped cream on top of the cake, then refrigerate the cake for an hour or so. If desired, sprinkle with a light dusting of cinnamon sugar before slicing.
Adding cornstarch to all-purpose flour creates cake flour. If you have cake flour on hand, you may use 1 1/2 cups of it in lieu of the all-purpose flour + cornstarch. If you don't have cornstarch or prefer not to use it, you may omit it from this recipe and use 1 1/2 cups of all-purpose flour instead.
The more holes you poke in the cake, the better the milk mixture will soak in. I prefer using the flat end of a wooden skewer for slightly bigger holes. But if you don't have a skewer, you may use a fork.
Half-and-half is a combination of 50% whole milk and 50% heavy cream, so you may make your own if you wish. Alternatively, you may replace the half-and-half in this recipe with whole milk for a slightly less rich cake.
For the fluffiest whipped cream, pop a metal bowl and metal beater in the freezer for about 15 minute to chill before whipping the cream.