Preheat the oven to 450°F (230°C). Line a baking sheet with parchment paper or grease it lightly.

Make the choux pastry: In a medium saucepan, bring water and butter to a boil. Once boiling, remove from heat and quickly stir in flour and salt all at once until the mixture forms a ball.

Add eggs: Return the pan to low heat and cook, stirring constantly for about 1 minute to dry out the dough slightly. Transfer to a mixing bowl and let cool for 5 minutes. Add eggs one at a time, beating vigorously after each addition until the dough is smooth and glossy.

Pipe the eclairs: Transfer the dough to a pastry bag fitted with a large round tip. Pipe 4-inch long strips about 1-inch wide onto the prepared baking sheet, leaving 2 inches between each eclair.

Bake: Place in the preheated oven and immediately reduce temperature to 375°F (190°C). Bake for 25-30 minutes until golden brown and puffed. They should feel light and hollow when done. Turn off the oven, prop the door open slightly, and let them cool in the oven for 10 minutes to prevent collapse.

Prepare pastry cream: While the eclairs are baking, heat milk and half the sugar in a saucepan until just simmering. Meanwhile, whisk egg yolks with remaining sugar in a bowl until pale yellow. Add cornstarch and salt, whisking until smooth.

Temper the eggs: Slowly pour about half the hot milk into the egg mixture while whisking constantly. Pour this mixture back into the remaining milk in the saucepan.

Cook the pastry cream: Cook over medium heat, whisking constantly, until the mixture thickens and comes to a boil. Continue to cook for 1-2 minutes more. Remove from heat and stir in vanilla and butter until smooth.

Cool the cream: Transfer to a bowl, press plastic wrap directly onto the surface to prevent a skin from forming, and refrigerate until completely cool, at least 1 hour.

Make chocolate glaze: Heat heavy cream until just simmering. Pour over chopped chocolate and let stand 2 minutes. Add butter and corn syrup (if using), then stir until smooth and glossy. Allow to cool slightly until thickened but still pourable.

Fill the eclairs: Once pastry shells have cooled completely, use a small knife to create a small hole at one end of each eclair. Fill a pastry bag fitted with a small round tip with the chilled pastry cream and pipe it into each eclair through the hole until full.

Glaze: Dip the top of each filled eclair into the chocolate glaze, allowing excess to drip off. Place on a wire rack to set.

Chill: Refrigerate the eclairs for at least 1 hour before serving to allow the flavors to meld and the chocolate to set completely.