Preheat the oven to 350°F and grease a 9x13-inch baking pan with cooking spray.
In a medium-sized bowl, sift together the cake flour, baking powder, and salt. Set aside.
3 cups cake flour, 1 tablespoon baking powder, 1 teaspoon salt
Using a stand mixer, cream the brown sugar and butter together until light and fluffy.
½ cup unsalted butter, 1¾ cups light brown sugar
Add the vanilla and oil to the mixing bowl and mix until combined.
½ cup vegetable oil, 2 teaspoons vanilla extract
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.
¾ cup creamy peanut butter
Add the eggs one at a time, mixing after each addition just until combined.
4 large eggs
Add the dry ingredients in three parts, alternating with the milk, starting and finishing with the flour mixture. Mix in the last part of flour by hand to prevent over mixing the batter.
1¼ cup whole milk
Pour the batter into the prepared baking sheet.
Bake for 28 to 32 minutes or until a cake tester comes out clean.
Remove from the oven and allow to cool completely before frosting, about 1 hour.