Preheat oven to 350°F (175°C). Grease and flour two 9-inch cake pans.
Whisk together cake flour, baking powder, and salt in a bowl.
Beat butter and sugar until light and fluffy; add eggs one at a time.
Mix in strawberry puree and vanilla extract.
Alternate adding flour mixture and milk; fold in diced strawberries.
Divide batter into pans and bake for 25–30 minutes; test with a toothpick.
Cool cakes in pans 10 mins; remove to racks to cool completely.
Beat cream cheese and butter; add powdered sugar, vanilla, and cream until smooth.
Frost cooled cakes and serve.