Preheat the oven to 350F. Butter 2 (9-inch) round cake pans, or spray with baking spray. Line the bottoms with parchment paper.

In a large bowl, whisk together the flour, baking powder, salt, and baking soda.

In a large mixing bowl or the bowl of a stand mixer with the paddle attachment, beat the butter on medium speed just until creamy. Add the sugar and beat until light and fluffy, about 5 minutes.

Scrape down the bowl and add the egg whites and vanilla. Beat until well combined and very fluffy.

Reduce the speed to low. Add the flour mixture alternating with the milk and the strawberry reduction, mixing just until combined.

Divide the batter among the two cake pans.

Bake for 30 minutes or until the cake is springy to the touch and starts to pull away from the sides of the pans. Let the cakes cool in the pans for 20 minutes. Remove and let cool completely on a wire rack.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, butter, vanilla, and salt until smooth and fluffy, about 5 minutes.

With the mixer on low, gradually add in the powdered sugar alternating with a tablespoon of the strawberry puree. Once all of the sugar is added, increase the speed to medium and beat until fluffy.

Place a cake layer on a cake stand. Spread about 1 cup of frosting on top of the cake. Top with the second layer. Spread the remaining frosting all over the outside of the cake and decorate as desired.