Preheat oven to 350°F and grease a half baking sheet (13x18-inches) with butter or nonstick spray.
In a mixing bowl or the bowl of a stand mixer, beat the butter, granulated sugar, brown sugar, and peanut butter until light and creamy.
Add eggs and vanilla and beat once more to combine, scraping down the sides of the bowl as needed.
Mix in the flour, baking powder, and salt until just combined, then press the mixture into the prepared pan with a spatula.
Bake until the edges are just golden brown and the center has barely set, about 15 minutes. Take care not to over bake.
While bars cool, make the frosting: Beat the butter, powdered sugar, cocoa powder, milk, and vanilla, until smooth.
Spread evenly over the bars. Let set, then cut into squares and serve. Enjoy!
