Pre-heat oven to 350 degrees. Line a 9-inch cake pan with parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt.
In the bowl of a stand mixer or in a large bowl with a hand mixer, cream together butter and both sugars until light and fluffy.
Add eggs and vanilla and mix to combine.
Add the flour mixture to the wet ingredients and mix until just combined.
Fold in the Reese's Pieces and peanut butter chips.
Press cookie dough into the prepared pan, as evenly as possible.
Bake at 350 degrees for 22-25 minutes, until edges are turning golden, but cookie is still nice and gooey in the middle.
Remove from oven and set on a wire rack to cool. Once cooled, use a knife to loosen edges of cookie and turn out onto a cake plate or platter.
Put frosting in a pastry bag and pipe along the edges. Add additional Reese's Pieces if desired.