Step 1: Preparing the Choux Pastry

1. Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
2. In a saucepan over medium heat, combine water, milk, butter, sugar, and salt. Bring to a simmer until butter melts.
3. Remove from heat and quickly stir in flour, mixing until a dough forms.
4. Return to heat and cook for 1-2 minutes, stirring continuously until the dough pulls away from the pan.
5. Transfer dough to a mixing bowl and let cool for 5 minutes.
6. Add eggs one at a time, mixing thoroughly after each addition. The dough should be smooth and pipeable.
7. Transfer to a piping bag fitted with a large round tip. Pipe 4-inch strips onto the prepared baking sheet.
8. Bake for 25-30 minutes or until golden brown and puffed. Let cool completely.

Step 2: Making the Lemon Pastry Cream

1. Heat milk in a saucepan over medium heat until steaming but not boiling.
2. In a separate bowl, whisk sugar, egg yolks, and cornstarch until smooth.
3. Gradually whisk the hot milk into the egg mixture to temper it.
4. Return mixture to the saucepan and cook over medium heat, stirring constantly until thickened.
5. Remove from heat and stir in butter, lemon zest, lemon juice, and vanilla extract.
6. Cover with plastic wrap (directly on the surface) and refrigerate until chilled.

Step 3: Filling the Éclairs

1. Cut éclairs in half horizontally or create a small hole on one end.
2. Transfer lemon pastry cream to a piping bag fitted with a small round tip.
3. Pipe the cream into each éclair shell until full.

Step 4: Preparing the Lemon Glaze

1. In a small bowl, whisk together powdered sugar, lemon juice, and zest until smooth.
2. Adjust consistency by adding more lemon juice if needed.

Step 5: Assembling the Éclairs

1. Dip the top of each éclair into the lemon glaze.
2. Let set for a few minutes before serving.