Using a stand mixer fitted with a paddle, mix flour, sugar, baking powder and salt on low speed until combined. Add the butter, 1 piece at a time, and mix until only pea-sized pieces remain.
Add all but 1/2 cup of the milk mixture to the dry ingredients. Increase speed to medium-high and beat until light and fluffy. Reduce speed to medium-low and add the remaining 1/2 cup of milk mixture. Beat until incorporated. Give it a final stir by hand.
Divide the batter evenly between prepared pans. Smooth tops with a spatula and gently tap the pans on the counter to settle the batter.
Bake 23-25 minutes, until a toothpick inserted in the center comes out clean or a probe thermometer reads 200℉
Let the cakes cool in the pans on a wire rack for 10 minutes. Remove the cakes from the pans, remove the parchment and, let them cool completely on a rack.
Vanilla Pastry Cream
Mix the egg yolks, sugar, and cornstarch in a bowl. Whisk until the sugar is dissolved and the eggs are fluffy and light in color.
5 large egg yolks, ½ cup granulated sugar, 2 tablespoons corn starch
Pour the milk and cream into a saucepan. Add the vanilla bean. Bring to a simmer over medium heat. Remove the mixture from the heat and remove the vanilla bean.
1 cup whole milk, 1 cup heavy cream, 1 vanilla bean
Add a ladle of the heated milk mixture to the whipped eggs. Quickly whisk the eggs so the hot milk doesn't cook the eggs.
Pour the tempered eggs into the saucepan with the milk. Whisk until the mixture is combined.
Place the saucepan on the heat again, and gently heat the mixture while continually whisking until the mixture starts to thicken.
Remove the pot from the heat and continue to stir for another 2 minutes.
Transfer the pastry cream into a bowl. Let cool at room temperature. Once at room temperature, cover with plastic wrap (make sure the plastic wrap is pressed into the surface of the pastry cream. Refrigerate.
Assemble The Cake
Stack the cake layers. Add a thick slather of pastry cream and fruit between each layer.
Cover the entire cake with whipped cream, using it like icing.
Decorate the cake with whipped cream with berries. [The traditional approach is to cover the top with halved strawberries.]