Make the Strawberry Puree: First, wash, hull, and blend your strawberries until they are completely smooth.
Pour the smooth puree into a small saucepan. Simmer it over medium heat, stirring often to prevent it from sticking.
Cook until the puree has reduced by about half. This concentrates the flavor significantly. You should have about one cup of thick puree. Set the puree aside to cool completely before using it.
Prepare the Cake Batter: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. Line the bottoms with parchment paper to guarantee the cakes release easily.
In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
In a separate bowl using a stand mixer or electric hand mixer, beat the softened butter and granulated sugar until light and fluffy, which usually takes about 5 minutes.
Add the room temperature egg whites and vanilla extract, and beat for another minute until well combined.
With the mixer on low speed, add the flour mixture in three parts, alternating with the milk and a half cup of your cooled strawberry puree. Mix only until the batter just comes together.
Bake the Cake: Divide the batter evenly between your prepared cake pans.
Bake for about 30 minutes. You will know the cakes are done when a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 20 minutes before turning them out onto a wire rack to cool completely.
Mix the Frosting and Assemble: In a large bowl, beat the softened cream cheese and butter until smooth and creamy.
Add the vanilla and salt and mix well. With the mixer on low, gradually add the sifted powdered sugar, alternating with a quarter cup of the cooled strawberry puree.
Once everything is added, increase the speed to medium and beat until the frosting is light and fluffy.
Place one cooled cake layer on your serving plate. Spread about one cup of frosting evenly over the top.
Carefully place the second cake layer on top. Use the remaining frosting to cover the top and sides of the cake. You can create smooth sides or make decorative swirls with your spatula.