Preparation

• Preheat the Oven - Set the oven racks to upper-middle and lower-middle positions. Preheat to 425°F (218ºC). Line two sheet pans with parchment paper and set them aside.
• Make the Dough - In a large heavy-bottomed saucepan, add 1 cup of water, sugar, salt, and butter. Bring to a boil over medium-high heat and stir until the butter fully melts, about 2 minutes. Turn off the heat and immediately add the flour. Vigorously stir with a large spoon (non-metal) until the flour is incorporated. Increase the heat to medium, and constantly stir until it clumps together, about 4 to 5 minutes. The dough should look relatively dry and just begin to leave a film on the saucepan.
• Cool the Dough - Transfer the dough to a bowl of a stand mixer fitted with a paddle. Slowly stir on low speed (setting 2) to cool to 130°F (54ºC) or just below, about 2 to 3 minutes. This prevents the eggs from curdling when added.
• Add the Eggs in Stages - Add eggs one at a time, mixing on medium-low speed (setting 4) until each egg is fully incorporated, about 30 to 45 seconds per egg. Once 3 eggs are added, check to see if the dough pulls away from the bowl's sides in thick threads; it should be shiny but firm and not runny. If it’s still too thick, add the fourth egg and mix for 45 seconds.
• Piping the Dough - Add a large plain tip to a piping bag. Optionally grease the inside of the pastry bag with cooking spray. Add the dough to the pastry bag. Pipe onto the sheet pan, creating a 2-inch circular ball, spacing them at least 2 inches apart. Flatten any tails left on top when piping with a damp finger.
• Brush on Egg Wash - In a small bowl, whisk together one egg and 1 tablespoon of water. Brush the tops and sides of each dough ball with the egg wash.
• Gradual Baking Process - Bake for 10 minutes at each temperature setting: 425°F (218ºC), 375°F (191ºC), 325°F (163ºC), 275°F (135ºC), 225°F (107ºC), 200°F (93ºC). It will take about 60 to 70 minutes of total baking time. Transfer cooled shells to a cooling rack.
• Make the Whipped Cream - In a stand mixer fitted with the whisk attachment, add heavy cream, powdered sugar, and vanilla extract. Whip on medium-low speed until frothy, about 1 minute. Increase to medium-high speed and whip until smooth, stiff peaks form, about 2 minutes.
• Piping the Cream - Working in batches, add the whipped cream to a pastry bag fitted with a large star tip. Cut the shells in half and evenly pipe the whipped cream into the pastry bottoms. Gently place the lids on top.
• Top with Sugar - Sprinkle powdered sugar on top of each cream puff. Serve immediately, or refrigerate, uncovered, if not eating within one hour.