Make the Pastry Cream:

1. In a medium saucepan, heat the milk and ¼ cup sugar over medium heat until steaming and sugar dissolves. Don’t let it boil.
2. In a bowl, whisk together egg yolks, remaining ¼ cup sugar, and cornstarch until smooth and pale yellow.
3. Slowly pour about half the hot milk into the egg mixture while whisking constantly (this tempers the eggs). Then pour the egg mixture back into the saucepan with remaining milk.
4. Cook over medium heat, whisking constantly, until the mixture thickens and comes to a boil. Let it boil for 1 minute while whisking continuously – this cooks out the starchy taste.
5. Remove from heat and whisk in butter and vanilla until smooth. Pour through a fine-mesh strainer into a clean bowl.
6. Press plastic wrap directly onto the surface to prevent skin from forming. Refrigerate until completely cold, at least 2 hours or overnight.

Make the Choux Pastry:

7. Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper or a silicone mat.
8. In a medium saucepan, combine water, milk, butter, sugar, and salt. Bring to a rolling boil over medium-high heat, stirring occasionally to ensure butter melts.
9. Remove from heat and add all the flour at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan, about 1-2 minutes. A thin film will form on the bottom of the pan – this is good!
10. Transfer the dough to a mixing bowl (or continue in the pan if you prefer). Let cool for 5 minutes – the dough should be warm but not hot, or it will cook the eggs.
11. Add eggs one at a time, mixing vigorously after each addition. The dough will look separated and broken at first but will come together with continued mixing. After the last egg, the dough should be smooth, glossy, and slowly fall from the spoon in a thick ribbon. If it’s too stiff, beat another egg in a small bowl and add it gradually until you reach the right consistency.
12. Transfer dough to a piping bag fitted with a large round tip (or a gallon freezer bag with the corner cut off to create a ¾-inch opening).
13. Pipe 4-5 inch long strips of dough onto the prepared baking sheet, spacing them about 2 inches apart. You should get about 12 eclairs. Use a wet finger to smooth any peaks or points.
14. Bake at 425°F for 15 minutes, then reduce temperature to 375°F (190°C) without opening the oven door and bake for an additional 20-25 minutes until golden brown, puffed, and dry-looking. Don’t open the oven during baking or they may collapse!
15. Turn off oven, crack the door open slightly, and let eclairs sit in the cooling oven for 10 minutes. This dries them out and prevents collapse.
16. Remove from oven and transfer to a wire rack. Use a skewer or small knife to poke a few small holes in each eclair to release steam. Cool completely.

Make the Chocolate Glaze:

17. Place chopped chocolate in a heat-proof bowl. Heat the cream and butter in a small saucepan until just simmering.
18. Pour hot cream mixture over chocolate and let sit undisturbed for 1 minute. Then whisk until completely smooth and glossy. Stir in corn syrup if using. Let cool for 5-10 minutes until slightly thickened but still fluid.

Assemble the Eclairs:

19. Transfer cold pastry cream to a piping bag fitted with a small round tip (or use a zip-top bag with a small corner cut off).
20. Use the tip to poke 3 small holes along the bottom of each eclair shell. Pipe cream into each hole until the eclair feels full and heavy. You can also slice eclairs in half horizontally and pipe cream onto the bottom half, then replace the top.
21. Dip the top of each filled eclair into the chocolate glaze, letting excess drip back into the bowl. Place on a serving platter.
22. Refrigerate for at least 30 minutes to set the glaze before serving. Serve chilled or at cool room temperature.