In a medium mixing bowl, sift the cake flour. Add the baking powder and salt, then whisk for about 20 seconds. Set this mixture aside.
In the bowl of an electric stand mixer fitted with the paddle attachment (if your mixer doesn't have a paddle that scrapes the bowl while mixing, pause occasionally throughout the mixing process to scrape down the sides and bottom of the bowl), beat together the butter and sugar until they're pale and fluffy.
Mix in the eggs and egg yolks one at a time, adding the vanilla with the last egg yolk. Add 1/3 of the flour mixture at a time to the butter/egg mixture, alternating with 1/2 of the milk. Mix on low speed just until combined after each addition. Remember to scrape down the sides and bottom of the bowl and gently fold the batter several times.
Divide the batter among the prepared baking pans. Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool the cakes in the pans for about 5 minutes. Run a knife around the edges of the cakes to loosen them, then invert them onto wire racks to cool completely. I recommend transferring them to gallon-size resealable bags after about 25 minutes of cooling to prevent them from drying out. Let them finish cooling in the bags.
Once the cakes are cool, frost them with Strawberry Cream Cheese Whipped Cream. Store the cake in an airtight container in the refrigerator.