Prepare the pastry cream: Fill a large bowl with ice water, then place a fine sieve over a medium bowl. Set both ingredients aside.
In a 3- to 4-quart saucepan, whisk together the sugar, cornstarch, and salt. Whisk the egg yolks until well combined and all the dry ingredients are incorporated. Then, whisk the milk to combine.
Place a saucepan over medium-high heat, stirring constantly, until the custard begins to thicken noticeably, about 4 to 8 minutes. Once it reaches this point, observe if any large bubbles burst on the surface. Once this happens, stir constantly for 1 minute, then remove from heat.
Add the butter and vanilla, stir until melted and a smooth mass forms.
Strain the custard through a fine sieve into a medium bowl. Immediately press a piece of cling film onto the surface of the custard to prevent sheepskin from forming. Place the bowl with the custard in an ice bath to cool for 30 minutes. Transfer to the refrigerator and refrigerate for at least 4 hours or overnight.
Prepare the cabbage pie: Preheat the oven to 175°C. Line two baking trays with baking paper.
Pour the water, milk, butter, sugar, and salt into a medium saucepan. Place over high heat and bring to a boil.
Remove from heat and add flour at once. Using a wooden spoon or stiff silicone spatula, mix until the flour is well combined and there are no lumps, pressing and breaking the dough against the sides of the pan.
Return to the saucepan over medium-high heat and cook, stirring frequently, until the batter is combined into a single mass and a dry layer appears on the bottom and sides of the pan. If you have an instant-read thermometer, it should read 175 degrees Fahrenheit.
Transfer the batter to a bowl and beat on medium speed for about 2 minutes to cool. It should read 145 degrees on the thermometer for immediate reading.
Add the eggs one at a time, making sure each one is well mixed before adding the next. Once all the eggs have been added, scrape down the bottom and sides of the bowl and stir again to make sure everything is well combined, for an additional 5-10 seconds.
Use immediately or store at room temperature for up to 2 hours by placing dough in a piping bag or covering surface with plastic wrap.
Cook the éclairs: Transfer the choux pastry to a piping bag with a 1/2-inch round tip (I recommend Ateco #866). Hold the piping bag at a 45-degree angle and pull the tip slightly over the surface of the parchment paper to create 1-inch-wide, 4-inch-long cake lines. Squeeze 12 éclairs onto each baking sheet. Dip your finger in cold water and gently pat the irregularities.
