Preheat the oven to 325 degrees F. Lightly grease a 9-inch springform pan. (Note: You can also use a 9-inch cake pan, but it will work best if you line the bottom with parchment to make removing the cake easy.)
In the bowl of a stand mixer, beat together the butter and both sugars on high until light and fluffy, 2 to 3 minutes. Add the peanut butter and beat again until fully combined. Scrape down the sides of the bowl as needed.
Add the vanilla and then the eggs one at a time, mixing on low between each addition.
Sprinkle the baking soda and cornstarch over the batter and mix on low until no dry spots remain. With the mixer running on low, add the flour a little at a time until it is fully mixed in.
Stir in the Reese's pieces and chocolate chips.
Spread the batter out in the prepared pan, smoothing out the top. Scatter some extra Reese's pieces over the top of the cake (this is optional, but it always looks nice to have a few chocolates on top).
Bake until a knife inserted in the center comes out with a few moist crumbs, 32 to 34 minutes.
Allow the cake to cool completely before adding frosting.
To make the frosting, in a standing mixer fitted with the paddle attachment (or using a hand mixer), beat the butter, cocoa powder, honey, and peanut butter until smooth. Add the powdered sugar and mix on low until combined and then beat on high until the frosting is very smooth.
When the cookie cake is completely cool use a piping bag to pipe frosting around the perimeter of the cake. Slice and serve!