Preheat your oven to 350°F (175°C) and grease a baking pan.
In a mixing bowl, cream together the butter, granulated sugar, brown sugar, and 2 cups of peanut butter until smooth. Add eggs and vanilla extract, mixing well.
Gradually add the flour, oats, baking soda, and salt, mixing until combined.
Spread the mixture evenly in the prepared baking pan. Bake for 25 minutes or until golden brown.
For the frosting, beat together the softened butter, powdered sugar, cocoa powder, milk, and vanilla extract until smooth.
Spread the frosting over the cooled bars and cut into squares.
Notes
Store the bars in an airtight container for up to a week.