Preheat oven to 350 degrees F.

Wet ingredients: In a large mixing bowl, cream together the butter, sugar and brown sugar. Add the eggs, vanilla, and peanut butter and mix well.

Dry Ingredients: In a separate bowl mix together the dry ingredients.

Combine: Add dry ingredients to creamy mixture. Press firmly into a greased 9x13'' pan.

Bake at 350 degrees for 17-21 minutes or until no longer glossy, but just barely set in the center. Do not over-bake; they will harden as they cool. Allow to cool completely before frosting.

Spread Peanut Butter: Once cool, spread a thin layer of creamy peanut butter over the bars.

Chocolate Frosting: Add butter to a small skillet over medium heat. Once melted, stir in cocoa. Remove from heat and stir im milk, powdered sugar and vanilla. Whisk until smooth, using electric beaters to get out any lumps, if needed. Spread chocolate frosting over the top of the bars.