Preheat oven to 350 degrees. Oil sheet pan and set aside.

Place strawberries in a small food processor; process until pureed.

In a medium bowl, whisk together flour, baking powder, and salt; set aside. In a small bowl, mix together milk and strawberry puree; set aside.

In the bowl of an electric mixer fitted with the paddle attachment, cream butter on medium-high speed, until light and fluffy. Gradually add sugar and continue to beat until well combined and fluffy. Reduce the mixer speed to medium and slowly add eggs and egg whites until just blended. Add vanilla.

With the mixer on low, slowly add half the flour mixture; mix until just blended. Add the milk mixture; mix until just blended. Slowly add remaining flour mixture, scraping down sides of the bowl with a spatula, as necessary, until just blended.

Spread batter on prepared sheet pan. Transfer to oven and bake until top is just dry to the touch, 22 to 25 minutes. Transfer pan to a wire rack and let cool completely before icing.

With a mixer, whip cream, and set aside. In another bowl, mix cream cheese, sugar, vanilla, and salt. Whip until fluffy.

Gently fold in whipped cream in three additions, making sure to be short and gentle in order to not deflate whipped cream.

Store in fridge. Frost cake just before serving.