MAKE THE PASTRY CREAM (Can be done up to 2 days ahead):

1. Heat the milk: In a medium saucepan, heat the milk over medium heat until it just begins to simmer. Remove from heat and set aside.
2. Whisk egg mixture: In a separate bowl, whisk together the egg yolks and ¼ cup of sugar until pale and slightly thick, about 2 minutes. Add the cornstarch and salt, whisking until completely smooth with no lumps.
3. Temper the eggs: Slowly pour about ½ cup of the hot milk into the egg mixture while whisking constantly. This gradually raises the temperature of the eggs without scrambling them. Pour the tempered egg mixture back into the saucepan with the remaining milk, whisking constantly.
4. Cook the cream: Place the saucepan back over medium heat. Whisk constantly, making sure to reach all corners of the pan. The mixture will thicken suddenly—keep whisking vigorously for 1-2 minutes after it thickens to cook out the starchy flavor.
5. Finish and chill: Remove from heat and whisk in the butter, vanilla, and remaining ¼ cup sugar. Strain through a fine-mesh strainer into a clean bowl to remove any lumps. Press plastic wrap directly onto the surface to prevent a skin from forming. Refrigerate until completely cold, at least 2 hours or overnight.

MAKE THE CHOUX PASTRY:

6. Preheat and prepare: Preheat your oven to 425°F (220°C). Line two baking sheets with parchment paper. Optionally, use a ruler to draw 4-inch lines spaced 2 inches apart as guides for piping.
7. Make the dough: In a medium saucepan, combine water, butter, sugar, and salt. Bring to a full rolling boil over medium-high heat, ensuring the butter is completely melted.
8. Add flour: Remove from heat and immediately add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a cohesive ball and pulls away from the sides of the pan, about 1 minute.
9. Cook the dough: Return the pan to medium-low heat and cook, stirring constantly, for 2-3 minutes. This step is crucial—it dries out the dough and cooks the flour, which helps the éclairs puff properly. The dough should leave a thin film on the bottom of the pan.
10. Cool slightly: Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment (or use a hand mixer and large bowl). Beat on medium speed for about 1 minute to release some steam and cool the dough slightly. The bowl should feel warm but not hot to the touch.
11. Add eggs: With the mixer running on medium speed, add the eggs one at a time, beating well after each addition until fully incorporated. The dough will look broken at first but will come together. After the last egg, beat until the dough is smooth, glossy, and falls from the paddle in a thick ribbon.
12. Pipe the éclairs: Transfer the dough to a piping bag fitted with a large round tip (½-inch). Hold the bag at a 45-degree angle and pipe 4-inch long strips onto the prepared baking sheets, spacing them 2 inches apart. Use a wet finger to gently smooth any peaks.
13. Bake: Bake at 425°F for 15 minutes without opening the oven. Then reduce the temperature to 375°F (190°C) and continue baking for 15-20 minutes more until golden brown and firm to the touch. The éclairs should feel light and hollow.
14. Dry the shells: Turn off the oven. Use a sharp knife to poke a small hole in each end of each éclair to release steam. Return to the warm oven with the door slightly ajar for 10 minutes to dry out the interiors. Transfer to a wire rack to cool completely.

MAKE THE CHOCOLATE GANACHE:

15. Heat cream: In a small saucepan, heat the heavy cream over medium heat until it just begins to simmer. Remove from heat.
16. Melt chocolate: Place the chopped chocolate in a heatproof bowl. Pour the hot cream over the chocolate and let sit for 2 minutes without stirring.
17. Combine: Add the butter and corn syrup (if using), then whisk gently from the center outward until smooth and glossy. Let cool for 5-10 minutes until slightly thickened but still pourable.

ASSEMBLE THE ÉCLAIRS:

18. Fill the shells: Transfer the chilled pastry cream to a piping bag fitted with a small round tip (a Bismarck tip works best). Poke three small holes along the bottom of each éclair. Insert the piping tip into each hole and squeeze gently to fill, moving from one end to the other until you feel slight resistance.
19. Apply ganache: Dip the top of each filled éclair into the chocolate ganache, allowing excess to drip off. Run your finger along the edges for a clean finish. Alternatively, use an offset spatula to spread ganache on top.
20. Set and serve: Place the glazed éclairs on a rack or baking sheet. Let the ganache set at room temperature for 30 minutes, or refrigerate for 10 minutes. Serve immediately or refrigerate until ready to serve (best served within 6-8 hours of assembly).