Preheat oven to 350 degrees and prepare 3 eight-inch round or square cake pans by greasing and flouring the pans and then set aside
Combine and sift the flour, baking powder, and salt in a small bowl and set aside
Add the brown sugar and butter to the bowl of a standing mixer and mix on medium speed until pasty
Drizzle in the oil and mix on medium speed for 5 minutes; scrape down the bowl intermittently to ensure everything is mixed well.
Add the peanut butter and stir to combine on low speed
Add eggs one at a time, and mix until incorporated
Add the flour mixture in 3 parts to the mixer, alternating with the milk in 2 parts, beginning and ending with the flour; do not overmix. Mix only until the flour has been incorporated
Divide batter evenly among the 3 pans and bake for 28 to 33 minutes
When finished, remove cakes and cool in the pans for 30 minutes and then invert on wire rack to finish cooling right side up