Preheat your oven to 350°F (175°C).
Grease a 9x13-inch baking pan and line it with parchment paper.
Cream the butter, granulated sugar, and brown sugar in a large mixing bowl with an electric mixer until light and fluffy.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
Mix in the peanut butter until smooth.
In a separate bowl, whisk together the oats, flour, baking soda, and salt. Gradually mix into the wet ingredients.
Spread the batter evenly into the prepared baking pan.
Bake for 25-30 minutes, or until golden and a toothpick comes out clean. Cool in the pan for 10 minutes before transferring to a cooling rack.
Prepare the frosting by mixing the creamy peanut butter, softened butter, and cocoa powder until smooth.
Gradually add powdered sugar, vanilla extract, and enough milk to reach desired consistency.
Frost the cooled bars evenly with the peanut butter frosting.
Let the frosting set, then cut the bars into squares and serve.
