In a large saucepan, bring the water, butter, salt and sugar to a rolling boil over medium-high heat.
When it boils, immediately take the pan off the heat. Stirring with a wooden spoon, add all the flour at once and stir hard until all the flour is incorporated 30 to 60 seconds.
Return to the heat and cook, stirring, 30 seconds.
Scrape the mixture into a mixer fitted with a paddle attachment (or use a hand mixer).
Mix at medium speed.
With the mixer running, add 3 eggs, 1 egg at a time.
Stop mixing after each addition to scrape down the sides of the bowl.
Mix until the dough is smooth and glossy and the eggs are completely incorporated.
The dough should be thick but should fall slowly and steadily from the beaters when you lift them out of the bowl. If the dough is still clinging to the beaters, add the remaining 1 egg and mix until incorporated.
Using a pastry bag fitted with a large plain tip, pipe fat dots spaced 2 inches apart onto a parchment-lined pan.
For the Filling:
In a medium saucepan, heat the milk and vanilla bean to a boil over medium heat.
Immediately turn off the heat and set aside to infuse for 15 minutes.
In a bowl, whisk the egg yolks and sugar until light and fluffy. Add the cornstarch and whisk vigorously until no lumps remain.
Whisk in 1/4 cup of the hot milk mixture until incorporated.
Whisk in the remaining hot milk mixture, reserving the saucepan. Pour the mixture through a strainer back into the saucepan.
Cook over medium-high heat, whisking constantly, until thickened and slowly boiling.
Remove from the heat and stir in the butter.
Let cool slightly. Cover with plastic wrap, lightly pressing the plastic against the surface to prevent a skin from forming.
Chill at least 2 hours or until ready to serve. The custard can be made up to 24 hours in advance. Refrigerate until 1 hour before using.
For the Egg Wash:
Egg Wash: In a bowl, whisk the egg and water together.
Brush the surface of each eclair with the egg wash.
Use your fingers to smooth out any bumps of points of dough that remain on the surface.
Bake 15 minutes, then reduce the heat to 375 degrees and bake until puffed up and light golden brown, about 25 minutes more. Try not to open the oven door too often during the baking. Let cool on the baking sheet.
Once cooled you can cut the puffs in half and pipe the pastry cream or you can poke a hole in the bottom and pipe through there.
For the glaze pour the hot cream over the chocolate, add the coffee and vanilla then stir and melt in the microwave. Stir again then set aside.
Once cooled, spoon the glaze over the profiteroles and garnish with crushed pistachios if desired. For the sake of this recipe, add green tea powder.