Preheat the oven to 350 degrees F and grease a 9x13 pan with cooking spray.
In a medium sized bowl, sift together the cake flour, baking powder, and salt.
Using a stand mixer, combine the brown sugar and butter together until it becomes light and fluffy.
Add the vanilla and oil to the mixing bowl and mix until combined.
Once combined, increase the speed to medium-high until the batter is once again light and fluffy.
Add the peanut butter and mix until combined.
Add the eggs one at a time.
Add the flour in 3 parts, alternating with the milk, starting and finishing with flour.
Once the final part of flour is ready to be added, finish mixing by hand to prevent over mixing the batter.
Pour the batter into the prepared baking sheet.
Bake for 28-32 minutes or until a cake tester comes out clean.