Prepare the Strawberry Puree: Hull the strawberries, place them in a blender, and puree on high for about 30 seconds, or until completely smooth.
Reduce the Puree: Transfer the strawberry puree to a small saucepan and bring it to a simmer over medium heat, stirring frequently. Continue cooking until the puree has reduced by about half, which takes about 25 minutes for fresh strawberries or up to 45 minutes for frozen strawberries. The finished reduction should yield about 1 cup. Cool the Reduction: Allow the strawberry reduction to cool completely before dividing it for use in the cake layers and frosting.
Prepare the Cake Pans: Preheat the oven to 350°F. Butter two 9-inch round cake pans or coat them with baking spray, then line the bottoms with parchment paper. If desired, wrap the pans with soaked fabric baking strips.
Combine the Dry Ingredients: In a large bowl, whisk together the flour, baking powder, salt, and baking soda until evenly combined.
Cream the Butter: Place the softened butter in a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed just until creamy.
Add the Sugar: Add the granulated sugar to the butter and continue beating for about 5 minutes, until the mixture is light and fluffy.
Incorporate the Egg Whites: Scrape down the sides of the bowl, then add the egg whites and vanilla. Beat on medium speed for about 1 minute, until thoroughly combined and very fluffy.
Build the Batter: Reduce the mixer speed to low. Add the dry ingredients alternately with the room-temperature milk and strawberry reduction, mixing only until the ingredients are combined. Stop to scrape down the bowl as needed.
Color the Batter: If desired, mix in a drop or two of pink food coloring, keeping the addition optional.
Fill the Pans: Divide the finished batter evenly between the two prepared cake pans.
Bake the Cake: Bake at 350°F for 30 minutes, or until the cakes feel springy when touched and begin pulling away from the sides of the pans.
Cool the Layers: Let the cakes cool in their pans for 20 minutes. Remove them from the pans and transfer them to a wire rack to cool completely. Once removed, discard the parchment paper.
Beat the Frosting Base: In a large mixing bowl or stand mixer fitted with the paddle attachment, beat the room-temperature cream cheese, butter, vanilla, and salt for about 5 minutes, until smooth and fluffy.
Add the Sugar: With the mixer running on low, gradually add the sifted powdered sugar, alternating it with a tablespoon of the strawberry puree. Stop and scrape down the bowl several times as needed.
Finish the Frosting: Once all the powdered sugar has been incorporated, increase the mixer speed to medium and beat until the frosting is fluffy. If it is too stiff and lacks a silky consistency, add another tablespoon or two of strawberry puree or milk.
Layer the Cake: Place one completely cooled cake layer on a cake stand and spread about 1 cup of frosting evenly over the top.
Complete the Cake: Place the second cake layer on top. Use the remaining frosting to cover the outside of the cake, then decorate as desired.
Store the Cake: Keep the finished cake covered. According to the source recipe, it will keep at room temperature for up to 5 days.
