Wash and hull strawberries; puree in a blender then cook over low heat until reduced by half (about 15 minutes). Cool the puree completely.
Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
In a bowl, sift flour, baking powder, baking soda, and salt.
In a separate bowl, cream butter and sugar until light and fluffy. Add egg whites one at a time, beating well after each addition.
Stir in sour cream or yogurt, vanilla, and milk. Fold in reduced strawberry puree.
Alternately add dry ingredients and strawberry puree mixture to the batter, mixing until just combined.
Divide batter evenly between prepared pans. Bake 25-28 minutes until a toothpick inserted in the center comes out clean.
Cool cakes completely in pans. Meanwhile, make cream cheese frosting: beat cream cheese and butter until smooth, gradually add powdered sugar and vanilla extract.
Assemble the cake by layering frosting between and on top of cooled cake layers.