Preheat oven to 350°F. Line a 9x9-inch pan with parchment paper.
Blend fresh strawberries until lightly pureed. Set aside.
In a medium bowl, whisk together the all-purpose flour, cake flour, baking powder, baking soda, and salt.
In a large bowl, whisk together the melted butter and sugar until smooth. Add the eggs one at a time, whisking well after each addition. Stir in the strawberry puree and vanilla extract.
Gently fold the dry ingredients into the wet ingredients until just combined. Do not overmix.
Pour the batter into the prepared pan and smooth the top. Bake for 40–45 minutes.
Strawberry Cream Cheese Frosting
In a small pan, add chopped strawberries, sugar, and a squeeze of lemon juice. Bring to a boil, then reduce heat and simmer for 10 minutes until thickened. Blend until smooth and let cool completely.
In a bowl, whisk the cream cheese and butter until smooth and fluffy, about 1 minute. Add powdered sugar and whisk until fully combined. Fold in strawberry puree.
Once the cake is completely cool, spread the strawberry cream cheese frosting evenly over the top.
Optional: garnish with freeze-dried strawberries and fresh strawberries.