Make the Pate a Choux (Choux Pastry): Preheat oven to 350 degrees F. Line two baking sheets with parchment paper.
Place the water, milk, butter, sugar, and salt in a medium saucepan. Place over high heat and bring to a full rolling boil.
Remove from the heat and add the flour all at once. Using a wooden spoon or stiff silicone spatula and stir until the flour is thoroughly mixed in and no lumps remain, pressing and smashing the dough against the sides of the pan.
Return the pot to medium-high heat and cook, stirring frequently, until the dough comes together into one mass and there is a dry film on the bottom and sides of the pan. If you have an instant-read thermometer, it should register 175 degrees F.
Transfer the dough to a mixing bowl and beat on medium speed for about 2 minutes to cool the dough down. It should register 145 degrees on an instant-read thermometer.
Add the eggs one at a time, ensuring each one is fully incorporated before adding the next. Once all of the eggs have been added, scrape down the bottom and sides of the bowl and mix again to ensure everything is fully incorporated, an additional 5 to 10 seconds.
Use immediately or keep at room temperature for up to 2 hours in a piping bag or with a piece of plastic wrap pressed against the surface.
Bake the Eclairs: Transfer the choux pastry to a piping bag fitted with a ½-inch round piping tip (I recommend Ateco #866). Hold the pastry bag at a 45-degree angle and lightly drag the tip along the surface of the parchment paper to create 1-inch wide by 4-inch long lines of pastry dough. Pipe 12 eclairs onto each baking sheet. Dip a finger in cold water and gently pat down any bumps.
Bake the sheets one at a time until the eclairs are puffed, golden brown, and feel light and hollow when picked up, 28 to 32 minutes.
Remove from the oven and while the eclairs are still hot (you may need to use a paper towel to handle them), and using a paring knife, make two ¼-inch holes in the bottom of each eclair (one near each end) by inserting the tip and turning in a circular motion.
Once both sheets have been baked and holes poked in the bottom, return both pans to the still-warm oven. Prop the door open with a wooden spoon and allow the eclairs to set in there for 30 minutes. Remove from the oven and cool completely before filling.
