In the bowl of a stand mixer, cream butter and sugars until fluffy. Add eggs, one at a time, beating well after each addition. Add peanut butter and vanilla and mix until incorporated.
In a separate bowl, combine flour, salt, and baking powder. Add all at once to peanut butter mixture and mix well. Using a rubber spatula, pat mixture onto a 17.25 x 11.5-inch rimmed baking sheet.
Bake for 25 to 30 minutes or until the top is set and a toothpick inserted comes out clean.
Make the glaze while bars bake: In a stand mixer combine powdered sugar, cocoa powder, and butter. Mix until moistened. Add vanilla, then mix. Add milk, 1 tablespoon at a time, until spreading consistency.