Start by pureeing the strawberries in a blender until completely smooth. Pour mixture into medium saucepan and set over low heat. Stir occasionally as the mixture reduces and thickens. It will take about 30 minutes to reduce the mixture by half. Remove from heat and set aside to cool.
Preheat oven to 350 degrees. Prepare 3 9-inch round cake pans by spraying with nonstick spray and lining with a round cut out of parchment paper. Set aside. In a medium bowl, mix cake flour, baking powder, baking soda, and salt. Set aside.
Add sugar and butter to a mixing bowl fit for a stand mixer. Using the paddle attachment, cream together until light and fluffy, about 3 minutes. Add sour cream and mix until combined. Add half of egg whites and mix until combined. Add rest of egg whites, vanilla extract, and cooled strawberry puree and mix until combined.
Add 1/3 of dry ingredients to batter and mix until combined. Add half of milk and mix until combined. Add another 1/3 of dry ingredients and mix until combined. Add rest of milk and mix. Finally, add last 1/3 of dry ingredients and mix until smooth.
Split batter evenly among the 3 prepared pans and spread tops smooth. Bake cakes in preheated oven until set, about 20 minutes. Remove from oven and let cool about 10 minutes. Then, remove from pan and place on a flat surface (like a baking sheet or clean counter) to cool completely before assembling the cake.