Filling: Heat milk and vanilla bean to a boil over medium heat. Turn off the heat and infuse for 15 minutes. In a bowl, whisk the egg yolks and sugar until light and fluffy. Add cornstarch and whisk until no lumps remain. Whisk in 1/4 cup of the hot milk mixture until incorporated. Whisk in the remaining milk. Pour the mixture through a strainer back into the saucepan. Cook over medium-high heat, whisking constantly, until thickened and slowly boiling. Remove from heat and stir in butter. Let cool slightly. Cover with plastic pressing against the surface to prevent a skin from forming. Chill at least 2 hours. Can be made a day ahead.

Pastry: Preheat the oven to 425. Line sheet pan with parchment. In a large saucepan, bring water, butter, salt and sugar to a rolling boil. 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. Mix at medium speed. With the mixer running, add 3 eggs, 1 at a time. Stop after each addition to scrape down the sides. Mix until smooth and glossy. Dough should be thick, but should fall slowly from the beaters when you lift them out of the bowl. If the dough is still clinging to the beaters, add remaining egg

Using a pastry bag fitted with a large plain tip, pipe fat lengths of dough (about the size and shape of a short hot dog) onto the lined baking sheet, leaving 2 inches of space between them. You should have 15 lengths.

Egg Wash: Whisk the egg and water together. Brush surface of each eclair. Bake 15 minutes, then reduce to 375 degrees until puffed and golden brown, about 25 minutes more. Dont open door too often. Cool on baking sheet.

Fit a medium-size plain pastry tip over your index finger and use it to make a hole in the end of each eclair (or just use your fingertip). Using a pastry bag fitted with a medium-size plain tip, gently pipe the custard into the eclairs, using only just enough to fill the inside (dont stuff them full).

Glaze: In a small saucepan, heat the cream over medium heat just until it boils. Immediately turn off the heat. Put the chocolate in a medium bowl. Pour the hot cream over the chocolate and whisk until melted and smooth. Set aside and keep warm. The glaze can be made up to 48 hours in advance. Cover and refrigerate until ready to use, and rewarm in a microwave or over hot water when ready to use.

Dip the tops of the eclairs in the warm chocolate glaze and set on a sheet pan. Chill, uncovered, at least 1 hour to set the glaze. Serve chilled.