Preheat the oven to 375℉ (190℃) conventional (see note 1 if using a convection oven). Line 2 baking trays with parchment paper and set aside.
In a medium saucepan, combine the water, milk, butter, sugar, and salt. Place over medium heat, stirring occasionally until the butter has fully melted and the mixture just comes to a boil.
Remove the saucepan from the heat and immediately add the flour all at once. Using a spatula, stir vigorously until a smooth dough forms and no dry flour remains.
Return the saucepan to low-medium heat and cook, stirring constantly (but gently), for 1–2 minutes, or until the dough forms a ball, pulls away from the sides of the pan, and leaves a thin film on the bottom of the saucepan. Avoid overcooking the dough, as this can cause the butter to separate.
Transfer the dough to a large mixing bowl and add the vanilla. Using a hand mixer or stand mixer fitted with the paddle attachment, mix on a low speed for about 1 minute to cool the dough slightly. The dough should feel warm, but not hot. If necessary, allow it to cool for a few more minutes before adding the eggs.
In a separate bowl, whisk the eggs until well combined. With the mixer on a low speed, add about one-quarter of the egg mixture to the dough and mix until fully incorporated. Add another quarter and mix again. Continue adding the remaining egg mixture a little at a time, mixing well after each addition and checking the consistency as you go. Depending on factors such as humidity and how much the dough was cooked, you may not need all of the egg mixture. The dough is ready when it is smooth and glossy and slowly falls from a spatula in a thick V-shaped ribbon. It should hold its shape while still having a little movement.
Transfer the dough to a piping bag fitted with a large round piping tip (I used a 1A tip). Pipe 2-inch (5 cm) rounds onto the prepared baking trays, leaving enough space between each one for them to expand. Shape them slightly taller rather than wider to encourage a nice rise.
Dip your finger into a little water and gently smooth down any peaks on top of the dough. Lightly dust the tops with powdered sugar.
Bake one tray at a time on the lower third rack of the oven for 30–35 minutes, or until the cream puffs are deep golden brown, feel light in weight, and sound hollow when tapped.
Turn the oven off, crack the oven door open slightly, and leave the cream puffs inside for 10 minutes. Transfer them to a wire rack to cool completely. Turn the oven back on, wait until it is preheated and repeat the baking process with the remaining tray.