Preheat your oven to 425°F. Line a large, flat baking sheet with parchment paper or a silicone baking mat and set it aside.

In a medium saucepan, combine the 1 stick of cubed unsalted butter, 1 cup of water, and ¼ teaspoon of salt. Place the pan over medium-high heat and bring the liquid to a full, rolling boil so the butter melts completely.

The exact moment the liquid boils, dump the 1 cup of all-purpose flour into the pan all at once. Immediately reduce the heat to low and stir vigorously with a sturdy wooden spoon.

Continue stirring continuously for 1 to 2 minutes. The flour will rapidly absorb the liquid and pull away from the sides of the pan to form a smooth, cohesive dough ball. A thin film should coat the bottom of the pan. Remove the pan from the heat source and let the hot dough cool down for 5 minutes.

Transfer the warm dough ball into a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment.

With the mixer running on medium speed, add the room-temperature eggs one at a time, beating thoroughly after each addition until the egg is completely absorbed into the paste before adding the next. Once all 4 eggs are incorporated, the dough should look thick, glossy, and form a smooth "V" shape when lifted on the spatula.

Fit a pastry bag with a large round tip (or simply use a gallon-sized zip-top bag with the corner snipped off) and scrape the glossy dough inside.

Pipe the dough onto your prepared baking sheet into 12 to 14 uniform mounds, roughly 2 inches in diameter, leaving 2 inches of space between each round to allow for massive steam expansion. Use a clean finger dipped in water to gently smooth down any sharp pointed tips on top of the dough.

Place the baking sheet on the middle oven rack and bake at 425°F for exactly 20 minutes. Without opening the oven door, reduce the heat to 375°F and bake for an additional 10 to 15 minutes until the pastry puffs look completely crisp and take on a deep, even golden-brown color.

Remove the shells from the oven. Immediately poke a small slit or hole into the side of each puff with a toothpick or sharp knife to let the trapped internal steam escape; this step ensures the interiors dry out completely without turning soggy. Set them on a wire rack to cool down to room temperature.

While the shells cool, assemble the sweet filling. In a large chilled mixing bowl, combine the cold heavy whipping cream, sifted powdered sugar, and vanilla extract. Beat with an electric hand mixer on high speed for 3 to 4 minutes until stiff, stable peaks form.

Use a sharp serrated knife to carefully slice the top third off each cooled pastry shell. Spoon or pipe the sweet whipped cream generously into the hollow bottoms, then place the pastry caps gently back over the cream. Dust the tops with a snowy layer of powdered sugar right before serving cold.