Preheat the oven to 375°F or 190°C and grease a 9×13 inch rimmed baking pan well.
Melt the butter and peanut butter together until smooth and glossy.
Stir in the sugar, then whisk in the eggs, milk, and vanilla until combined.
Mix in the flour, baking soda, and salt just until smooth, loosening with a little milk if needed.
Spread the batter evenly in the pan and bake for 15 to 18 minutes until lightly golden at the edges.
Whisk powdered sugar, milk, vanilla, and peanut butter until a thick, spreadable frosting forms.
Spread frosting over the warm bars, let set, then slice and serve.