Chocolate Eclairs

To make the filling:

1. Pour the milk into a medium saucepan set over medium heat. Warm just until the milk barely begins to steam, being careful not to boil.
2. In a medium bowl, whisk the egg yolks and sugar until very well combined and light in color. Add the cornstarch and whisk vigorously until no lumps remain. Gradually whisk a ladle of the hot milk mixture into the egg mixture. Gradually whisk in the remaining hot milk mixture. Pour the egg-milk mixture back into the saucepan. Cook over medium-high heat, whisking constantly, until thickened and barely boiling.
3. Remove from heat and stir in the butter and vanilla. Strain into a clean bowl. Let cool slightly before pressing plastic wrap directly against the surface. Chill for at least 2 hours, or preferably overnight.

For the pastry:

1. Preheat the oven to 425°F. Line a sheet pan with parchment paper.
2. In a large saucepan set over medium-high heat, combine 1 cup water, the butter, salt, and sugar and bring to a rolling boil. Immediately remove from heat. Vigorously whisk in all the flour at once and whisk for about 30 seconds, until combined. Return to heat and cook for 30 seconds, stirring with a silicone spatula until the mixture is more dry and begins to stick to the bottom of the pan.
3. Scoop the mixture into a stand mixer fitted with the paddle attachment, or use a hand mixer. Turn to medium speed and beat for about 30 seconds. Add 3 of the eggs, one at a time, mixing well after each addition. Mix until the dough is smooth and glossy and the eggs are thoroughly incorporated. Scrape down the sides and bottom of the bowl at least once. The dough should be thick but fall into a V-shaped ribbon when the paddle is lifted. If the dough is too thick, beat the remaining 1 egg into a separate small bowl, and drizzle in just enough until that V-shaped ribbony consistency is achieved.
4. Fit a pastry bag with a large plain tip and transfer the dough to the bag. Pipe 10 to 12 large logs about 1-inch wide and 4-inches long onto the prepared parchment-lined baking sheet, spacing about 2 inches apart. Whisk the remaining egg with 2 teaspoons water and brush over the éclairs. Gently smooth any bumps on the dough with your fingers.
5. Bake for 15 minutes at 425°F, then reduce the heat to 375°F, rotate the pan, and continue baking for another 25 minutes, or until puffed and golden brown. Allow to cool completely on the baking sheet.
6. MAKE AHEAD: At this point, the baked and cooled pastry shells can be frozen until hardened, then removed to an airtight container. Store in a safe place in the freezer for up to 1 month. Let thaw to room temperature then refresh them in a 350°F oven for 3 to 5 minutes before proceeding with glazing and filling.

To make the chocolate glaze:

1. Place the chocolate in a heatproof bowl. Microwave the cream just until boiling, about 30 seconds. Immediately pour the hot cream over the chocolate and stir until melted. Add in the vanilla and corn syrup.

To finish:

1. Split each éclair shell in half lengthwise. Take the top shell and dip into the chocolate glaze, letting the excess drip off. Place, glazed side up, on a parchment-lined baking sheet. Using a spoon or pastry bag, fill the bottom shell with the pastry cream. Once the glaze has set on the top shells, place them on top of the pastry cream. Serve or store in the fridge, covered, for up to 2 days.