Preheat oven to 350F degrees. Line a 11 x 15 inch jelly roll pan with aluminum foil and spray with non-stick cooking spray. Set aside.
In a small bowl, whisk together flour, baking soda, and salt. Set aside.
n a large mixing bowl, cream together butter, granulated sugar, brown sugar, peanut butter, eggs, and vanilla until light and fluffy.
Gradually add the dry ingredients. DO NOT OVERMIX!
Stir in quick oats.
Spread peanut butter mixture into prepared pan. Bake for 15 minutes or until lightly brown. Cool for 10 minutes (I placed the whole pan in the fridge to speed up this process).
MAKE CHOCOLATE FROSTING:
Whip remaining creamy peanut butter until it becomes light and fluffy. Carefully spread on top of semi-cool peanut butter bars.
Mix the butter, milk, cocoa powder, vanilla extract, and powdered sugar together until frosting is light and fluffy.
Place a scoop of chocolate frosting on several spots on top of the whipped peanut butter. This helps so you aren't dragging the frosting around and messing with the whipped peanut butter layer.
Carefully spread the chocolate frosting almost to the edge of the bars. Let frosting set for another 10-15 minutes before cutting bars into squares.
Notes
Store bars in an airtight container at room temperature or in the fridge for up to 5 days.