Place a race in the center of the oven and preheat oven to 350 degrees F.
Lightly spray three 9-inch round cake pans with cooking spray, then dust them with flour. Shake out the excess flour. Set the pans aside.
Place the cake mix, peanut butter, oil, eggs, and vanilla in a large mixing bowl. Add 1 1/3 cups water, then beat with an electric mixer on low speed until blended 30 seconds. Stop the machine and scrape down the side of the bowl with a rubber spatula. Increase the mixer speed to medium and beat for 2 minutes longer, scraping down the side again if necessary. The batter should be well blended. Divide the batter among the prepared pans, smoothing it out with a rubber spatula. Place the pans in the oven side by side or, if your oven is not large enough, place two on the center rack and the third pan in the center of the highest rack.
Bake until the cakes spring back when lightly pressed with a finger, 18 to 20 minutes. Check the pan on the highest rack first as it will bake the quickest and may need to be rotated to a lower rack while it bakes. Remove the cakes from the oven, and place them on wire racks to cool for 10 minutes. Run a knife around the edge of each later and invert onto a rack and then invert onto another rack so that the cakes are right side up. Allow the cakes to cool completely.
Meanwhile, place 28 of the peanut butter cups into the freezer for 15 to 20 minutes so they will be easier to chop, then finely chop them and set aside with the whole peanut butter cups.
Make the frosting: Place the butter and peanut butter in a large mixing bowl and beat with an electric mixer on low speed until creamy. Add 2 cups confectioners' sugar, 1/4 cup milk and the vanilla and beat on low speed until the mixture is combined. Add 1 1/2 cups confectioners' sugar and the remaining 1/4 cup milk and beat the frosting until it is smooth and spreadable. Then, increase the mixer speed to high and beat, adding the remaining 1/2 cup sugar a little at a time until the frosting is thick and fluffy.
To assemble the cake, place one cake layer, right side up, on a serving plate and spread some of the frosting over the top. Press half of the chopped Reese's into this frosting, distributing them evenly. Place a second cake layer, right side up, on top of the first. Spread some of the frosting over the top. Press the remaining chopped Reese's into this frosting. Place the third cake layer, right side up, on top of the second layer, then frost the top smoothly and generously. Frost the side of the cake with smooth, clean strokes. Place the remaining whole peanut butter cups decoratively around the edge of the cake.