Prepare the Choux Pastry:

1. Preheat the Oven: Preheat your oven to 400°F (200°C). Line two baking sheets with parchment paper or silicone baking mats.
2. Make the Choux Dough: In a medium saucepan, combine the water, butter, sugar, and salt. Bring to a boil over medium heat, stirring occasionally. Once the butter is melted, add the flour all at once, stirring vigorously until the dough comes together and pulls away from the sides of the pan.
3. Add the Eggs: Remove the dough from heat and let it cool for a couple of minutes. Gradually add the eggs, one at a time, mixing well after each addition until the dough is smooth and glossy.
4. Pipe the Pastry: Transfer the dough to a piping bag fitted with a large round tip. Pipe 3-4 inch long strips of dough onto the prepared baking sheets, spacing them about 2 inches apart.
5. Bake the Eclairs: Bake the eclairs in the preheated oven for 20-25 minutes, or until they are puffed and golden brown. Avoid opening the oven door during the first 15 minutes of baking to ensure they rise properly.
6. Cool the Pastry: Once baked, turn off the oven and let the eclairs cool inside with the door slightly ajar for 10 minutes. Then remove them from the oven and cool completely on a wire rack.

Prepare the Strawberry Custard Filling:

7. Heat the Milk and Cream: In a medium saucepan, heat the milk and cream over medium heat until it begins to simmer.
8. Whisk the Egg Yolks and Sugar: In a separate bowl, whisk together the egg yolks, sugar, and cornstarch until smooth.
9. Temper the Egg Mixture: Gradually add the hot milk mixture to the egg yolk mixture, whisking constantly to avoid curdling the eggs. Once combined, return the mixture to the saucepan and cook over medium heat, whisking constantly until it thickens.
10. Add the Strawberry Puree: Once the custard has thickened, remove it from the heat and stir in the vanilla extract and pureed strawberries. Let it cool to room temperature, then refrigerate for at least 30 minutes to set.

Prepare the Strawberry Glaze:

11. Make the Glaze: In a small bowl, whisk together the powdered sugar and strawberry puree until smooth. Add milk, one teaspoon at a time, until the glaze reaches a thick but pourable consistency.

Assemble the Eclairs:

12. Fill the Eclairs: Once the choux pastry shells have cooled, use a small sharp knife to cut a slit along the side of each eclair. Fill a piping bag with the strawberry custard filling and pipe it into the center of each pastry.
13. Top with Glaze: Dip the top of each filled eclair into the strawberry glaze, allowing the excess to drip off.
14. Chill the Eclairs: Place the eclairs in the refrigerator for 30 minutes to allow the glaze to set.