Make the Choux Pastry
Preheat oven to 400°F. In a medium saucepan, bring water, butter, sugar, and salt to a boil over moderate heat. Remove pan from heat. Add flour and stir vigorously with a wooden spoon for about 2 minutes, until dough comes together and a film forms on the bottom of the pan. Transfer dough to a large bowl and beat at medium speed until slightly cooled, about 1 minute. Add eggs, 1 at a time, beating well after each addition.
Transfer dough to a pastry bag fitted with a 1-inch round tip. Pipe 12 (5-inch-long) logs onto a parchment-lined baking sheet. Bake for 10 minutes. Turn oven down to 325°F and bake shells for 30 minutes longer, until golden brown. Transfer to a rack and let cool.
Make the Pastry Cream
In a medium saucepan, bring milk, vanilla bean, and seeds just to a boil. Meanwhile, in a large bowl, whisk sugar with cake flour and salt. Whisk in egg and egg yolks. Slowly add hot milk, whisking constantly. Pour mixture back into saucepan and bring to a boil over moderate heat, whisking constantly. Continue to boil pastry cream, whisking constantly, until thick, about 30 seconds longer. Immediately strain pastry cream through a fine sieve into a medium bowl. Cover with plastic wrap and refrigerate for at least 30 minutes, or until cool.
In a medium bowl, whip heavy cream until soft peaks form. Whisk pastry cream, then fold in whipped cream until blended.
Make the Chocolate Glaze
In a medium bowl, melt chocolate in the microwave at 50% power, being careful not to overheat it. Whisk in butter until smooth.
Assemble the chocolate éclairs
With a serrated knife, split éclair shells lengthwise. Spoon a generous amount of the pastry cream into the bottom half of each shell. Dip top half of each shell into the chocolate glaze, close éclairs, and serve.
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