Add the strawberries to a small saucepan. Heat on medium-low and mash the strawberries as you cook. Continue to cook the strawberries until it is cooked down to about ½ cup. Allow to cool completely.
Add the freeze-dried strawberries to a food processor or blender and process until it is a fine powder.
Preheat the oven to 350F. Grease and flour your 9x13 baking pan and line the bottom with parchment paper. Set aside.
Add the flour, baking powder, baking soda salt, and strawberry powder together and stir well. Set aside.
Add the butter, oil, cooled strawberry puree and sugar together. Beat well until well-combined.
Add the eggs and vanilla to the butter mixture and beat well for about 4 minutes.
Mix together the buttermilk and sour cream in a small bowl.
Add ⅓ of the flour mixture to the butter mixture and stir until just combined. Add in half the buttermilk mixture and stir until just combined. Add half the remaining flour, then the remaining buttermilk and stir until just combined. Add the remaining flour and mix until just combined.
Pour the batter into the baking sheet and spread evenly. Bake for 35 - 40 minutes, or until a toothpick comes out with a few crumbs clinging to it.
Allow the cake to cool completely and make the frosting.
Frosting
Put your freeze-dried strawberries and salt in a food processor and pulse until the strawberries become a fine powder.
Place your butter and cream cheese in a mixer and beat until smooth. Add in the powdered freeze-dried strawberries.
Add your powdered sugar one cup at a time, beating well between each addition.
Add in the vanilla extract and beat well.
Mix in the heavy cream one tablespoon at a time until you reach your desired consistency.
Allow the frosting to sit for a couple of minutes before spreading on your cooled cake.