In a medium saucepan, whisk together the sugar, cocoa powder, cornstarch, salt, and pumpkin pie spice. Gradually whisk in the milk.
Stir continuously while cooking the mixture over medium heat until it comes to a boil. It will take several minutes. Once it begins to boil, continue stirring and cooking for an additional minute. Remove it from the heat and whisk in the pumpkin puree, vanilla extract, and butter.
Transfer the pudding to a medium mixing bowl and press a piece of plastic wrap right up against the pudding to keep it from developing a skin on top. Cool in the refrigerator for at least four hours.
Before serving, whip together the heavy cream and sugar on high until soft peaks begin to form. Top each bowl with a small amount of whip cream and a little more pumpkin spice on top.