Heat the milk in the microwave until hot but not boiling.

In a large bowl, whisk together the egg yolks, sugar and cornstarch until smooth. Gradually add 1 cup of hot milk, whisking constantly until incorporated. Gradually add the remaining milk, whisking constantly.

Transfer the mixture into the saucepan and cook over medium-low heat, stirring constantly, for 8 minutes (or until thickened). Do not let the mixture boil (if bubbles start forming, reduce heat).

Remove the custard from heat and stir in butter and vanilla. Mix until fully combined. Let cool, then refrigerate. Chill the filling for at least 1 hour.

Preheat the oven to 425F. Line a baking sheet with parchment paper.

Put the water, butter, salt and sugar in a large saucepan and bring to a boil. Once it boils, take the saucepan off the heat and add the flour and quickly vigorously with a spoon until all the flour is incorporated. Return the saucepan to heat and cook, stirring, for 30 seconds.

Transfer the mixture into a large bowl and mix with a mixer on medium speed. Add 4 eggs (1 egg at a time) with the mixer running, scraping the sides of the bowl after each egg is added. Mix until smooth.

Put the dough in a pastry bag fitted with a large plain tip (or in a ziploc bag with a corner cut off) and pipe onto a baking sheet in the shape and size of a hot dog. Leave at least 2 inches of space between each piece of dough.

Whisk 1 egg in a small bowl. Brush the dough pieces with the egg.

Put the eclair dough in the oven and bake for 15 minutes. Reduce the heat to 375F and bake for 25 minutes.

Remove the eclair pastries from the oven and let cool.

Put the filling in a pastry bag fitted with a plain pastry tip. Poke a hole at the end of each eclair pastry and fill with the custard filling.

Put heavy cream and chocolate pieces in a small saucepan. Heat, stirring, over medium heat until the chocolate is fully melted and incorporated in the cream. Do not let the mixture boil.

Using a large spoon, put the chocolate glaze on top of eclairs. Chill uncovered for 1 hour to set the glaze.