Combine the water, butter, sugar, and salt in a saucepan and bring it to a rolling boil. Once the butter melts completely, dump in the flour all at once and stir vigorously with a wooden spoon. Keep stirring over low heat until the dough pulls away from the sides of the pan and forms a smooth ball, about 1 to 2 minutes.
Let the dough cool for about 5 minutes so it doesn't scramble the eggs. Then add the eggs one at a time, beating well after each addition until fully incorporated. The finished dough should look glossy, smooth, and thick enough to hold a soft peak when lifted.
Preheat your oven to 425°F and line a baking sheet with parchment paper. Spoon or pipe the dough into 12 evenly sized mounds, leaving space between each one. Bake for 15 minutes, then reduce the heat to 350°F and continue baking for 15 more minutes until golden brown and firm.
Once baked, poke a small slit in the side of each puff with a knife to release steam, then transfer them to a wire rack. Let them cool completely before filling warm puffs will melt the cream filling and turn soggy fast. This step takes patience, but it's worth it.
While the puffs cool, beat the chilled heavy cream in a cold bowl until soft peaks start to form. Add the powdered sugar, pumpkin puree, vanilla, cinnamon, nutmeg, ginger, and salt, then continue whipping until the mixture holds firm, fluffy peaks. Chill the filling for at least an hour if time allows.
Slice each cooled puff in half horizontally with a serrated knife. Pipe or spoon a generous amount of pumpkin cream into the bottom half, then gently place the top back on. Dust with powdered sugar right before serving for that classic bakery finish.