Make the choux pastry: Preheat the oven to 425°F (220°C). In a medium saucepan, combine water, butter, sugar, and salt, and bring to a boil. Once boiling, add flour all at once, stir vigorously, and cook until the dough pulls away from the pan. Remove from heat, let cool for 5 minutes, and add eggs one at a time, mixing well. Pipe the dough into 4-inch long strips on a baking sheet. Bake for 20 minutes, reduce temperature to 375°F (190°C) for another 10-15 minutes, until golden and crisp. Cool completely.

1. Make the custard filling: Heat milk in a saucepan until simmering. In a bowl, whisk together egg yolks, sugar, and cornstarch. Gradually add hot milk to the egg mixture, whisking constantly. Return to the saucepan, cook until thickened, then stir in vanilla and butter. Let cool to room temperature, then refrigerate for at least 1 hour.
2. Make the chocolate glaze: Heat cream in a saucepan until simmering, remove from heat, and add chopped chocolate and butter. Stir until smooth and glossy. Set aside to cool slightly.
3. Assemble the eclairs: Once the eclairs are cool, make a slit along the side or poke a hole in the end and fill with chilled custard using a piping bag. Dip or spoon chocolate glaze over the top of each eclair, covering the entire top. Let the chocolate set for 10-15 minutes.
4. Serve: Serve the eclairs fresh! They are best enjoyed the same day, though they can be stored in the refrigerator for up to 2 days.