Heat oven to 350℉ (175℃).
Spray three 8-inch round pans with baking spray. Set aside.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
With an electric mixer, beat butter, cookie butter, and both sugars until light and fluffy, about 2-3 minutes.
Add eggs, one at a time, beating well after each addition.
Add flour mixture alternately with milk, beginning and ending with flour.
Stir in vanilla.
Divide evenly among prepared pans.
Bake for 35 minutes, or until cake tests done.