Preheat your oven to 350°F. Grease two 9-inch round cake pans with butter or baking spray, then line the bottoms with parchment paper. For even baking, consider wrapping the cake pans with soaked fabric baking strips.
In a large bowl, combine the flour, baking powder, salt, and baking soda, and whisk thoroughly to blend. In another large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until it becomes creamy. Add the sugar and continue beating until the mixture is light and fluffy, about 5 minutes.
Scrape down the sides of the bowl, then add the egg whites and vanilla extract. Beat on medium speed until the mixture is well combined and very fluffy, about 1 minute. Lower the mixer speed and add the flour mixture alternately with the milk and the strawberry reduction, mixing just until combined. Be sure to scrape down the bowl as needed. If you like, add a drop or two of pink food coloring to enhance the cake's color. Divide the batter evenly between the prepared cake pans.
Bake for about 30 minutes, or until the cakes spring back when touched and begin to pull away from the sides of the pans. Allow the cakes to cool in the pans for 20 minutes before removing them to cool completely on a wire rack. Discard the parchment paper.