Place the cake flour, all-purpose flour, sugar, baking powder, baking soda, and salt in the bowl of an electric mixer, and stir on low speed to combine.

Add the butter, mixing on medium-low speed until the mixture resembles damp sand. {about 1 minute}

Add the eggs, one at a time, scraping the bottom and sides of the bowl to be sure all of the ingredients are fully incorporated.

Add the yogurt, milk, and vanilla.

Mix on medium speed for 2 to 3 minutes, to aerate the batter and build the cake's structure.

Divide the batter equally between the prepared pans, and bake for 30 to 40 minutes, or until a toothpick inserted in the thickest part of the cake comes out clean or with a few moist crumbs.

Cool completely before filling and frosting.