Preheat oven to 350F and line 13x9 pan with parchment paper or with foil sprayed lightly with no-stick spray.
In KitchenAid or with electric hand mixer, cream together butter and peanut butter.
Beat in sugars until well-combined.
Beat in eggs, one at a time.
Stir in vanilla extract.
In separate bowl, whisk together flour, baking powder, and salt.
Gradually, on low speed, add flour mixture to peanut butter mixture, pausing occasionally to scrape down sides of bowl.
Add milk and stir until combined.
Spread batter into prepared ban and bake on 350F for 25-28 minutes (toothpick inserted in center should come back mostly dry with only a few crumbs)
Allow to cool completely
Cut and brush with melted chocolate, if desired.