To make the sheet cake: Preheat oven to 350 degrees. Grease a sheet pan with cooking spray and set aside. I use an 11 x 17 jelly roll pan.
In a large mixing bowl, whisk together sugar, flour, baking soda, and salt. In a separate bowl, whisk together eggs, buttermilk, and vanilla extract. Set aside.
In a small sauce pan, melt the butter on medium-low heat. Whisk in the cocoa powder and hot water. Turn up the heat to medium-high and bring the mixture to a boil. Add the melted butter mixture to the dry ingredients and mix until smooth. Stir in the egg mixture and mix until ingredients are combined.
Pour the batter into the prepared sheet pan and tap on the counter a few times to distribute the cake batter evenly. Bake the cake for 18 minutes, or until a toothpick comes out clean when inserted in the center.
While the cake is baking, make the peanut butter frosting. In the bowl of a stand mixer, combine the sifted powdered sugar, milk, peanut butter, and vanilla extract. Beat with the beater blade until smooth. Frost the chocolate sheet cake after the cake has cooled. Sprinkle chopped up Reese's Peanut Butter Cups over the frosting, if desired. Let the frosted cake cool to room temperature. Cut into squares and serve.