Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper.

In a medium saucepan, combine 1/2 cup milk, water, 1/2 cup butter, 1 tsp sugar, and salt. Bring to a rolling boil over medium heat.

Add the flour all at once and stir vigorously with a wooden spoon until a dough forms and pulls away from the sides of the pan. Continue to cook and stir for 2 minutes to dehydrate the dough.

Transfer the dough to a stand mixer bowl. Beat on low speed for 1 minute to cool. Add eggs one at a time, beating thoroughly after each addition until the batter is smooth and glossy.

Transfer dough to a piping bag fitted with a large 1/2-inch round tip. Pipe 4-inch long logs onto the baking sheet, spaced 2 inches apart.

Bake at 400°F for 15 minutes, then reduce heat to 375°F (190°C) and bake for 20 more minutes until golden brown. Prick each shell with a toothpick to release steam and cool completely on a wire rack.

To make pastry cream: Whisk egg yolks, 1/2 cup sugar, and cornstarch in a bowl. Heat 2 cups milk until simmering, then slowly whisk into the egg mixture to temper. Return to the pan and cook over medium heat, whisking constantly until thick and boiling.

Remove pastry cream from heat; stir in 2 tbsp butter and vanilla. Transfer to a bowl, cover with plastic wrap touching the surface, and chill for at least 1 hour.

To make glaze: Heat heavy cream until just simmering, pour over chopped chocolate, let sit for 5 minutes, then whisk until smooth.

Fit a piping bag with a small round tip and fill with chilled pastry cream. Poke two holes in the bottom of each cooled shell and pipe in the cream until full. Dip the tops of the eclairs into the chocolate glaze and let set.