Preheat oven to 350 degrees. Line a 9x13 cake pan with parchment paper, or spray with a non stick baking spray. Set aside.
Add the freeze dried strawberries to the food processor and pulse until it is a fine powder.
Spoon the freeze dried strawberry powder to a large mixing bowl. Add the flour, baking powder, baking soda, and salt. Stir to combine.
In a medium size bowl add the 1 and 1/2 cup of the strawberry puree (keep the remaining 1/4 cup for the frosting), sugar, eggs, vanilla and oil. Stir to combine.
Add the wet ingredients to the dry and gently stir the batter together until just mixed.
Pour into the cake pan and bake for 40 minutes or until a toothpick inserted in the center comes out clean. Let the cake cool while you prepare the frosting.
Strawberries and Cream Frosting
Add the remaining 1/4 cup of strawberry puree to a small saucepan. Heat this over medium heat until the sauce begins to bubble, reduce the heat to low and let simmer while stirring until the amount has reduced down to about 2 tablespoons. This can take about 5 minutes. Remove from the heat and allow this to cool to room temperature. Can place in a bowl and store in the refrigerator if needed to help cool down.
In a medium size bowl add the cream cheese and butter. Mix until combined and smooth.
Add in the vanilla extract and the cooled down reduced strawberry puree (don't add more than 2 tablespoons, this will make the frosting runny). Mix to combine.
Add in the powdered sugar. Mix to combine. If frosting is too soft, add more powdered sugar. If it seems too stiff you can add a small amount of milk if needed.
Spread onto the top of the cake. Store the cake at room temperature in a sealed container.
If you don't have cake flour you can substitute with all purpose flour. You can also make your own homemade cake flour by removing 5 tablespoons of flour from the 2 and 1/2 cups and replacing that with cornstarch. Sift this mixture together.