Preheat the oven to 350F and grease and line a 9?13 baking pan with a strip of parchment paper.

Puree the strawberries using a food processor until almost completely pureed but with a few small chunks remaining.

In a bowl, whisk together the all purpose flour, cake flour, baking powder, baking soda, and salt.

In a large bowl, whisk together the vegetable oil, granulated sugar, eggs, strawberry puree, and vanilla extract.

Fold in the dry ingredients just until the batter comes together.

Pour the batter into the prepared pan and spread it evenly.

Bake for 35-40 minutes or until a toothpick in the center comes out clean with a few moist crumbs.

Let the cake cool completely in the pan before frosting. Refrigerate for at least an hour if you wish to lift the cake out of the pan.

To make the frosting, mix together the cream cheese and butter until smooth using a mixer.

Gradually mix in the powdered sugar, one cup at a time, followed by the strawberry puree.

Refrigerate the frosting for an hour to thicken.

Once the cake is completely cooled, spread the frosting on top and serve. Store in the fridge for up to 7 days.