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Preheat the oven to 425°F. Lightly grease (or line with parchment) two baking sheets.
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To make the choux pastry (éclair shells): Combine the water, butter, and salt in a medium-sized saucepan, heat until the butter has melted, and bring to a rolling boil.
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Remove the pan from the heat, and add the flour all at once, stirring vigorously.
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Return the pan to the burner and cook over medium heat, stirring all the while, until the mixture smooths out and follows the spoon around the pan; this should take less than a minute.
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Remove the pan from the heat, and let the mixture cool for 5 to 10 minutes. It'll still feel hot, but you should be able to hold a finger in it for a few seconds. If you have a digital thermometer, the temperature should be below 125°F.
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Transfer the mixture to a mixer, and beat in the eggs one at a time; it'll look curdled at first, but when you add the last egg it should become smooth. Beat for at least 2 minutes after adding the last egg.
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If you have a pastry bag, pipe the batter into 5" logs about 3/4" in diameter. Or simply use a spoon or cookie scoop to drop small mounds of the batter in a 5" line, gently spreading them into one solid pastry.
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Bake the pastries for 15 minutes, then reduce the oven temperature to 350°F and bake for an additional 25 minutes, until pastries are a medium golden brown. Don't open the oven door while the pastries are baking.
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Remove the pastries from the oven. Make a small slit in the top of each, and return them to the oven for 5 minutes, to allow the steam to escape. Place them on a rack to cool. When they're cool enough to handle, split each in half to make top and bottom pieces; splitting and exposing the centers to air will help keep them from becoming soggy.
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To make the pastry cream: Combine the sugar and cornstarch in a mixing bowl. Whisk in the yolks.
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Bring the milk and cocoa just to a simmer in a saucepan set over medium heat.
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Pour a quarter of the hot milk/chocolate into the yolk mixture, whisking until incorporated. Return the mixture to the saucepan over medium heat.
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Cook, stirring constantly, until the mixture becomes very thick, and just barely starts to boil. Remove the pan from the heat.
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Add the chocolate and butter, stirring until melted and smooth.
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Transfer the pastry cream to a bowl, and cover with plastic wrap. Cool to room temperature, then refrigerate for about 2 hours.
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To make the glaze: Combine the chocolate and corn syrup in a medium bowl.
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Heat the cream to simmering, then pour over the chocolate, stirring until melted and smooth. If the glaze seems thin, let it cool and set a bit before using.
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To assemble the éclairs: Pipe or spoon the cream into the pastries, then dip the tops of each one into the glaze. For best results, serve immediately; or refrigerate and serve within several hours.
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Store any leftover éclairs, well-wrapped, in the refrigerator for a few days. They don't freeze well, so enjoy éclairs while they're fresh!