Preheat oven to 325 degrees and line a 15x11-inch pan with parchment paper.
In a large bowl, beat butter and peanut butter until smooth.
Beat in granulated sugar, brown sugar and the egg.
Add flour, baking soda, vanilla and salt and beat just until mixed.
Spread batter in prepared pan.Note: Batter will be thick. Spread it to the sides as best you can.
Bake for 16 to 18 minutes.
To make frosting, place butter and milk in a medium saucepan. Heat until butter is melted.
Add peanut butter, confectioners' sugar, vanilla, and salt. Stir over low heat until smooth.Pour over brownies. Let frosting set for 20 minutes before slicing.
Notes
Try sprinkling Reese's Pieces or chopped peanuts on top for a little decoration and extra flavor.