In a medium saucepan, combine the milk and vanilla bean (if using vanilla extract, add later). Bring to a gentle simmer over medium heat, then remove from heat and let steep for 10 minutes. Remove vanilla bean, scrape seeds back into milk.

In a separate bowl, whisk together egg yolks, granulated sugar, and cornstarch until pale and smooth.

Slowly pour about half of the hot milk mixture into the egg yolk mixture, whisking constantly to temper the eggs. Pour the tempered egg mixture back into the saucepan with the remaining milk. Cook over medium heat, whisking continuously, until the mixture thickens considerably and comes to a boil. Boil for 1 minute, still whisking, to ensure cornstarch is cooked.

Remove from heat. Stir in the cold butter until melted and fully incorporated. If using vanilla extract, stir it in now. Pour the pastry cream through a fine-mesh sieve into a clean bowl to remove any lumps. Cover the surface directly with plastic wrap to prevent a skin from forming. Refrigerate for at least 2 hours, or until thoroughly chilled and firm.

Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper.

In a heavy-bottomed saucepan, combine water, butter, salt, and sugar. Bring to a rolling boil over medium-high heat, ensuring all butter is melted.

Remove from heat. Add the sifted flour all at once, stirring vigorously with a wooden spoon or rubber spatula until the mixture comes together to form a ball and pulls away from the sides of the pan. Return to medium-low heat and cook, stirring constantly, for 1-2 minutes to dry out the paste (this is called a panade). A thin film should form on the bottom of the pan.

Transfer the panade to a stand mixer bowl fitted with the paddle attachment (or use a hand mixer). Beat on low speed for 1-2 minutes to cool slightly. Gradually add the lightly beaten eggs, one at a time, beating well after each addition until fully incorporated. Scrape down the sides of the bowl as needed. The dough should be smooth, glossy, and fall slowly from the paddle in a V-shape. It should be thick enough to hold its shape but not too stiff.

Transfer the choux pastry to a piping bag fitted with a large star or round tip (about 1/2-inch opening). Pipe 4-5 inch long strips onto the prepared baking sheets, leaving about 2 inches between each éclair. You should get 10-12 éclairs.

Bake for 20 minutes at 400°F (200°C). DO NOT open the oven door during this time. Reduce oven temperature to 350°F (175°C) and continue baking for another 15-20 minutes, or until the éclairs are deeply golden brown, firm, and light when lifted. Turn off the oven, prop the door open slightly with a wooden spoon, and let the éclairs cool and dry out in the oven for an additional 10-15 minutes.

Remove from oven and transfer éclairs to a wire rack to cool completely before filling.

Place the finely chopped dark chocolate in a heatproof bowl. In a small saucepan, heat the heavy cream, butter, and corn syrup (if using) until just simmering. Remove from heat.

Pour the hot cream mixture over the chopped chocolate. Let stand for 2-3 minutes without stirring, then whisk gently from the center outwards until smooth and glossy. If the glaze is too thick, add a tiny bit more warm cream. Let it cool slightly until it's still pourable but not hot.

Once the éclairs are completely cool and the pastry cream is thoroughly chilled, transfer the pastry cream to a piping bag fitted with a small round tip (or a bismarck tip).

Using a small sharp knife, make 2-3 small holes on the underside of each éclair. Insert the piping tip into the holes and fill each éclair generously with pastry cream until it feels heavy and slightly firm.

Dip the top of each filled éclair into the chocolate glaze, allowing any excess to drip off. Place on a wire rack set over parchment paper to catch drips. Allow the glaze to set at room temperature or in the refrigerator for 15-20 minutes.