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

To puree the strawberries, place them in a food processor and let it run for a couple seconds, then pulse until almost completely pureed but with a few small chunks.

Whisk together the all purpose flour, cake flour, baking powder, baking soda, and salt in a bowl and set aside.

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

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

Pour it 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.

Make the frosting right when the cake is done baking so it can chill alongside the cake.

Using a hand or stand mixer, mix together the cream cheese and butter.

Mix in the powdered sugar 1 cup at a time, followed by the strawberry puree.

Refrigerate the frosting for an hour so it can thicken up.

Once the cake is completely cooled, spread the frosting on top. Serve right away or store in the fridge for up to 7 days.