Place the butter, water, and salt in a heavy saucepan, and bring to a full rolling boil. Stir in the flour and beat vigorously until the mixture forms a ball. Place the dough ball in a mixing bowl, and beat in the eggs, one at a time, adding the next egg when the last one has been fully incorporated.
Drop dough by tablespoons onto an ungreased baking sheet, and bake until the puffs rise and are golden brown on top, with fully-cooked insides, 20 to 25 minutes. Let cool before filling. Cut the cream puffs horizontally with a serrated knife.
To make filling, place the cream in the work bowl of an electric mixer, and whip until beginning to thicken, about 1 minute. Gradually add the confectioners' sugar and pumpkin pie spice until well-mixed, and continue mixing until the cream forms soft peaks, about 3 minutes.
Use a rubber spatula or wire whisk to fold 1/3 of the pumpkin puree into the whipped cream. Gently run the spatula through the center of the bowl, then around the sides of the bowl, repeating until fully incorporated. Add the remaining pumpkin puree, folding just until incorporated.
Spoon about 2 tablespoons of the pumpkin cream filling into each puff, and dust the top of each puff with confectioners' sugar and a pinch of pumpkin pie spice for garnish. Refrigerate leftovers.