Preheat oven to 350 degrees and line a 9x9 baking dish with parchment paper.
Cream the butter and peanut butter together. Add in the sugar and beat until well combined. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla.
In a small bowl, whisk together the flour, salt, and baking powder. Mix in to the peanut butter mixture until well combined.
Spread into the prepared baking dish.
Bake for 30 minutes or until a toothpick inserted near the center comes out clean. Cool completely before frosting.
For the chocolate frosting:
Add sugar, butter, and milk to a small saucepan over medium heat and bring to a boil. Boil for exactly 60 seconds and remove from heat. Stir in chocolate chips and continue stirring until the chocolate has melted.
Immediately pour over the peanut butter bars. Allow to cool for 30 minutes before cutting.