Make the Pastry Cream (prepare first):

1. In a medium saucepan, heat the milk over medium heat until it just begins to steam and small bubbles form around the edges. Don’t let it boil.
2. While the milk heats, whisk together the egg yolks, sugar, cornstarch, and salt in a medium bowl until smooth and pale yellow.
3. Once the milk is hot, slowly pour about half of it into the egg mixture while whisking constantly. This tempers the eggs and prevents them from scrambling.
4. Pour the egg-milk mixture back into the saucepan with the remaining milk. Cook over medium heat, whisking constantly, until the mixture thickens significantly and comes to a gentle boil, about 2-3 minutes. It should coat the back of a spoon thickly.
5. Remove from heat and whisk in the butter and vanilla extract until smooth. Strain the pastry cream through a fine-mesh strainer into a clean bowl to remove any lumps.
6. Press plastic wrap directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate for at least 2 hours until completely chilled and set.

Make the Choux Pastry:

7. Preheat your oven to 425°F (220°C). Line two baking sheets with parchment paper or silicone baking mats. If you like, you can draw guidelines on the parchment (4-inch lines spaced 2 inches apart) to help pipe uniform eclairs.
8. In a medium saucepan, combine the water, butter, sugar, and salt. Heat over medium-high heat until the butter melts completely and the mixture comes to a full rolling boil.
9. Remove the pan from heat and add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a ball and pulls away from the sides of the pan.
10. Return the pan to medium-low heat and cook, stirring constantly, for about 2 minutes. This dries out the dough slightly and cooks the flour, which helps create a better rise. The dough should look slightly glossy.
11. Transfer the dough to a mixing bowl (or the bowl of your stand mixer). Let it cool for about 3-4 minutes—it should be warm but not hot to the touch.
12. Add the eggs one at a time, beating well after each addition. The dough will look separated at first but will come together as you continue mixing. After adding 3 eggs, check the consistency. The dough should be smooth, glossy, and fall slowly from the spoon in a thick ribbon. If it’s still too stiff, beat the fourth egg in a separate bowl and add it gradually until you reach the right consistency. You might not need all of it.

Pipe and Bake:

13. Transfer the choux pastry to a piping bag fitted with a large round tip (about ½-inch opening). Pipe 4-inch long strips onto your prepared baking sheets, spacing them about 2 inches apart. You should get about 12 eclairs.
14. Use a damp finger to gently smooth any peaks or points on the piped dough—these can burn during baking.
15. Bake at 425°F (220°C) for 15 minutes, then reduce the temperature to 375°F (190°C) without opening the oven door. Continue baking for another 15-20 minutes until the eclairs are deeply golden brown and feel light and hollow when picked up. Don’t underbake or they’ll collapse!
16. Turn off the oven, crack the door slightly, and let the eclairs dry in the oven for 10 minutes. This helps ensure crispy shells.
17. Remove from the oven and transfer to a cooling rack. Use a sharp knife to poke a small hole in each end of each eclair to let steam escape. Let cool completely.

Make the Chocolate Glaze:

18. Place the chopped chocolate in a heatproof bowl. In a small saucepan, heat the heavy cream until it just begins to simmer.
19. Pour the hot cream over the chocolate and let sit for 1 minute. Add the butter and corn syrup (if using), then whisk until completely smooth and glossy. Let cool slightly until it thickens to a dipping consistency, about 5-10 minutes.

Assemble the Eclairs:

20. Once the pastry cream is chilled and the shells are completely cool, whisk the pastry cream until smooth. Transfer to a piping bag fitted with a small round tip.
21. Insert the piping tip into one of the holes you poked in each eclair. Gently squeeze the pastry cream into the shell, moving from one end to the other. You’ll feel the eclair become heavier as it fills. Repeat with all eclairs.
22. Dip the top of each filled eclair into the chocolate glaze, letting any excess drip off. Place on a rack or parchment paper to set.
23. Let the chocolate set at room temperature for about 30 minutes, or refrigerate for 10-15 minutes for faster setting.
24. Serve immediately for the crispest shells, or refrigerate until ready to serve (up to 4 hours ahead).