Preheat oven to 350 degrees and grease a 9x13-inch baking pan.
In a saucepan over medium heat, melt butter and brown sugar. Stir until smooth.
Take saucepan off heat, stir in peanut butter until smooth. Let cool.
In a large bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
Once peanut butter mixture has cooled, whisk in eggs one at a time. Stir in vanilla.
Add peanut butter mixture to dry ingredients, and stir until blended.
Stir in Reese's Pieces and pour batter into prepared pan. Bake for 25 to 30 minutes or until set in middle and golden brown around edges.
Make frosting. Combine butter, milk, and sugar in a saucepan and bring to a boil. Cook at a rolling boil for 30 seconds.
Remove from heat and stir in chocolate chips and vanilla until smooth. Pour over warm bars.
Sprinkle Reese's Pieces on top.