Make the reduced strawberry puree first, and let cool: In a blender or food processor, puree the fresh strawberries. You should have a little more than 1 cup (about 270g). Transfer the puree to a small saucepan over medium-low heat. Simmer, stirring occasionally, until it’s reduced to ½ cup (about 135g). This usually takes around 25–35 minutes. Remove from heat, pour into a heat-safe bowl, and cool completely before using.
Preheat the oven to 350°F (177°C). Grease two 9-inch round cake pans, line with parchment paper rounds, then grease the parchment paper.
In a medium bowl, whisk the cake flour, baking powder, baking soda, and salt together. Set aside.
In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter and sugar together on medium-high speed until light and creamy, about 3 minutes. Add the egg whites and beat on high speed until combined, about 2 minutes. Scrape down the sides of the bowl as needed. Add the sour cream and vanilla extract and beat on medium-high speed until combined, about 1 minute.
Add the dry ingredients and then, with the mixer running on low speed, slowly pour in the milk and beat until just combined. Whisk in the room-temperature reduced strawberry puree and food coloring (if using), making sure there are no lumps at the bottom of the bowl. The batter should be slightly thick.
Pour the batter evenly into the prepared cake pans and bake for 24–25 minutes or until a toothpick inserted in the center of the cake comes out clean.
Cool the cakes in the pans set on a cooling rack for 1 hour. Run a knife around the edges to loosen the sides, remove the cakes from the pan, peel off the parchment, and place on the rack to finish cooling.
In a blender or food processor, process the freeze-dried strawberries into a fine powder. If any larger bits remain, sift the powder through a fine-mesh sieve. Set aside.
In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and butter on medium-high speed until smooth, about 2 minutes. Add the confectioners’ sugar, strawberry powder, milk, and vanilla. Beat on low speed for 30 seconds, then gradually increase to high speed and beat for 3 minutes until completely combined and creamy.
To assemble, level the cakes: slice a thin layer off the tops of the cakes to create a flat surface. Place 1 cake layer on your cake stand and spread ¾–1 cup of frosting in an even layer on top. Top with the second layer upside down, and spread 1 cup of frosting all over the top and sides in a very thin layer to make a crumb coat. Refrigerate the cake until the crumb coat has set, about 20 minutes. Cover the top and sides with the remaining frosting.
Refrigerate the cake for at least 20 minutes to set the frosting before slicing.
Cover leftover cake tightly and store in the refrigerator for up to 5 days.