Preheat your oven to 350 degrees Fahrenheit (177 °C). Spray a 9x13 baking pan with baking spray and set aside.
To a large mixing bowl, add flour, baking powder, baking soda, and salt. Whisk the ingredients to combine and set aside.
To the bowl of a stand mixer fitted with the paddle attachment, add the oil, brown sugar, granulated sugar, and peanut butter. Mix the ingredients on medium (5-6 on a stand mixer) until combined, about 2-3 minutes.
Add in the eggs one at a time, beating to combine after each addition. Beat on medium-low after adding each egg until no more egg is visible.
Alternate adding the flour mixture and buttermilk to the peanut butter mixture, starting and ending with the flour. Beat on medium after each addition just until ingredients are combined. This means until no more dry flour or buttermilk are visible in the batter. Add vanilla and beat until just combined.
Pour batter into the prepared baking pan and smooth it out in an even layer with a silicone spatula. Transfer the pan to the preheated oven and bake for 25-30 minutes until a toothpick inserted into the center comes out with no wet batter.
Allow cake to cool for 10 minutes in the pan then transfer it to a wire rack to cool completely. Do this by very carefully turning the cake out onto parchment paper then carefully flipping it onto a parchment-lined wire cooling rack.
While the cake is cooling add the freeze-dried strawberries to a food processor and pulse until they form a fine powder and set aside.
Add butter to the bowl of a stand mixer fitted with the paddle attachment and beat on medium-high (speed of 7-8) until smooth and creamy, about 3 minutes. Add strawberries, powdered sugar, half and half or milk, vanilla, and salt to the mixer bowl and beat on low then gradually increase speed as powdered sugar mixes into the frosting.
Continue to beat until ingredients are combined and the frosting is smooth and creamy, about 1-2 minutes. Do not overmix the frosting as this can cause it to separate.
Spoon frosting out on top of the completely cooled cake and use a frosting spatula to smooth frosting out into an even layer over the cake. Slice and enjoy!