Preheat the oven to 350 degrees F. Grease and flour a 9-inch x 13-inch baking pan and set aside.
In a small bowl, sift together the flour, baking powder, baking soda, and salt; set aside.
In a stand mixer fitted with a paddle attachment (or using a hand mixer), cream the butter and sugar together until light and fluffy, about 4 minutes. Add the eggs one at a time, beating the batter for 30 seconds after each addition. Add the vanilla and beat well.
Gently fold the flour mixture into the butter mixture, mixing until just incorporated. Use a rubber spatula to fold the remaining flour in until well blended. Pour the batter into the prepared pan.
Bake for 22 to 25 minutes. Immediately use a bamboo skewer to poke the cake all over.
Three Milks
Whisk the three kinds of milk together in a large bowl or measuring cup, then pour over the top of the warm cake.
Return the cake to the off (but warm) oven for an additional 10 minutes, this helps the milk absorb.
Cover that cake and let sit until it reaches room temperature then transfer to the fridge for at least two hours before frosting.
Whipped Cream
Whip the cream, sugar, and vanilla together until stiff peaks form. Spread over the top of the cake, then sprinkle with cinnamon sugar. Keep refrigerated until serving.
Notes
All-purpose flour can be used instead of cake flour but the cake flour definitely yields a finer crumb.
Up to an additional 1/2 cup of whole milk can be added to the filling, any more than that and the milk starts to break down the structure of the cake.
It’s best to poke and add the milk to the cake when it’s warm as this helps the cake absorb the milk.