Preheat the oven to 350°F (177°C). Spray a 9x13 inch baking pan with cooking spray. Set aside.
In a large bowl (or the bowl of a stand mixer), sift the cake flour, sugar, baking powder, baking soda and salt. Whisk to combine. Add the butter, vanilla and ½ cup milk. Mix on medium speed for 1 minute. Scrape down the sides and bottom of the bowl with a spatula. The mixture will resemble a thick dough.
In a medium bowl, whisk together the remaining milk, yogurt and eggs. With the mixer speed on medium, add the egg mixture to the flour mixture in 3 additions, mixing for about 15 seconds after each addition. Scrape down the sides of the bowl as needed and mix for 15 seconds more, until the batter is just combined. Be careful not to over-mix.
Pour batter into prepared pan and spread evenly with a spatula. Bake in oven for 30-35 minutes or until a toothpick inserted into the center comes out clean. Begin checking for doneness at 28 minutes. Place cake onto a wire rack to cool completely in pan.
Once cake is completely cool, use a biscuit cutter to cut the individual cakes. You should get 12 rounds altogether. Place the rounds on a baking sheet and put them in the freezer for 30 minutes. After 30 minutes, they will be easy to slice in half with a sharp knife.