Preheat the oven to 400°F and line a large baking sheet with parchment paper.
In a medium saucepan, combine 125 g unsalted butter, 1 cup water, and a pinch of salt, and bring to a gentle boil over medium heat.
Remove the pan from the heat and add 1 cup all-purpose flour all at once, stirring quickly with a wooden spoon until no dry streaks remain.
Return the pan to low heat and cook the dough for 2 to 3 minutes, stirring and pressing it against the sides and bottom of the pan until it forms a smooth ball and leaves a thin film on the bottom.
Transfer the dough to a mixing bowl and let it cool for 5 to 7 minutes until warm but not hot to the touch.
Beat 4 large eggs in a small bowl, then add them to the warm dough in 3 to 4 additions, mixing well after each addition until the dough is smooth, shiny, and falls from the spoon in a thick V shape.
Spoon or pipe the choux dough into 12 equal mounds on the prepared baking sheet, spacing them slightly apart.
Bake for 20 to 25 minutes until the puffs are deeply golden, well risen, and feel light and hollow when gently lifted.
Turn the oven off, crack the oven door, and let the puffs sit inside for 10 minutes to dry, then transfer them to a wire rack to cool completely.
For the custard, place 2 cups whole milk and the split vanilla bean or vanilla bean paste in a medium saucepan and heat over medium heat until steaming with small bubbles around the edges, then remove from heat and let steep for 5 minutes.
In a separate bowl, whisk together 5 large egg yolks, 1/2 cup granulated sugar, and 2 tablespoons cornstarch until thick and pale.
Slowly pour the warm milk into the yolk mixture while whisking constantly to temper the eggs.
Return the mixture to the saucepan and cook over medium to medium low heat, whisking constantly and scraping the sides and corners, until the custard thickens, turns glossy, and just begins to bubble.
Remove the custard from the heat, whisk in 1 tablespoon unsalted butter until smooth, then pour into a clean bowl.
Press plastic wrap directly onto the surface of the custard and refrigerate until completely chilled and thick, about 1 hour.
In a chilled bowl, beat 1/2 cup cold heavy cream with 1 teaspoon powdered sugar until soft peaks form, then refrigerate until ready to use.
Once the puffs are cool, use a small sharp knife to cut a slit in the side of each puff or slice them in half horizontally.
Whisk the chilled custard to loosen it, then spoon it into a piping bag and pipe the custard into the centers of the cream puffs.
Pipe or spoon a small swirl of whipped cream on top of the custard in each puff.
Dust the filled cream puffs lightly with powdered sugar just before serving.