Preheat the oven to 200°C and line two baking sheets with parchment paper.
Combine water, milk, butter, sugar, and salt in a saucepan and bring to a full simmer over medium heat.
Remove from heat, add the sifted flour all at once, and stir vigorously until a dough forms.
Return the pan to medium heat and cook, stirring, until a film forms on the bottom and the dough looks satiny, about 2 minutes.
Transfer the hot dough to a mixing bowl and beat for 1 minute to cool slightly.
Beat in the eggs one at a time, mixing fully after each, until the dough is glossy and falls in a V from the spatula.
Fill a piping bag fitted with a 1 cm round tip and pipe 12 logs about 12 cm long, spacing well.
Smooth tips with a damp finger and brush lightly with beaten egg.
Bake at 200°C for 10 minutes, then reduce to 180°C and bake 20 to 25 minutes until deeply golden and puffed.
Turn off the oven, pierce each shell with a skewer, and let dry in the turned-off oven with the door cracked for 10 minutes.
Cool shells completely on a wire rack.
For coffee pastry cream, whisk yolks, sugar, cornstarch, and 1 tablespoon espresso powder in a bowl until thick.
Heat milk to a simmer, slowly whisk into the yolk mixture, then return to the saucepan.
Cook over medium heat, whisking constantly, until thick bubbles appear and the cream is glossy.
Remove from heat and whisk in butter, vanilla, and a pinch of salt, then press through a sieve into a bowl.
Cover the surface with plastic wrap and chill until cold, about 1 hour.
Whip 120 ml chilled heavy cream to soft peaks and fold into the cold coffee pastry cream.
Fit a piping bag with a small round tip and fill with the coffee cream.
Poke two small holes on the underside of each shell and pipe cream to fill until slightly heavy.
For glaze, heat 60 ml cream to steaming, stir in chocolate, 1 tablespoon espresso powder, corn syrup, and a pinch of salt until smooth.
Dip the tops of filled eclairs into the warm glaze, letting excess drip off, and set on a rack to firm.
Refrigerate eclairs for 20 to 30 minutes to set before serving.