Pour the milk and vanilla into a saucepan and bring to a boil. In a mixing bowl, whisk the egg yolks with the sugar. Add the cornstarch and mix well. Once the milk is boiling, add the chocolate and stir until melted. Pour the chocolate milk mixture into the egg mixture, mix, and return everything to the saucepan over low heat. Stir constantly until the pastry cream thickens.

In a saucepan, combine the water, milk, salt, sugar, and butter. Bring to a boil. Remove from heat and add the flour all at once, stirring with a wooden spoon until a thick dough forms. Return to low heat and cook the dough for a few seconds to dry it out. Beat the eggs in a separate bowl, then gradually add them to the dough, mixing well after each addition.

Using a piping bag fitted with a 1 cm tip, pipe 3-inch long strips onto a baking sheet. Lightly brush with beaten egg.

Bake in a preheated oven at 350°F (180°C) for 20 to 25 minutes.

Melt the chocolate. Heat the cream in a saucepan. Pour the hot cream over the chocolate in three additions, stirring well each time. Add the butter and mix until smooth.

Fill the éclairs with pastry cream.

Dip the tops of the éclairs into the chocolate glaze, then refrigerate.