Preheat oven to 350 degrees F. In a large mixing bowl, cream together the butter, sugar and brown sugar.
Add the eggs, vanilla, and peanut butter and mix well.
In a separate bowl mix together the dry ingredients. Add dry ingredients to creamy mixture.
Press firmly into a greased 9x13'' pan. Bake at 350 degrees for 17-21 minutes. Do not over-bake! They will look just barely set in the center, and they will harden as they cool. Allow to cool completely.
Once cooled, spread a thin layer of peanut butter over the bars.
To make the chocolate frosting:
Add butter to a small skillet over medium heat. Once melted, stir in cocoa.
Remove from heat and add 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.
Make Ahead and Freezing Instructions: Peanut Butter Bars will keep well for up to 1 week, stored in an airtight container in the fridge. Freeze, covered well, for up to 3 months. Thaw overnight in the refrigerator, then bring to room temperature before serving.