In a medium saucepan, combine water, whole milk, unsalted butter, granulated sugar, and salt. Bring to a vigorous boil over medium heat, then reduce heat and add all-purpose flour, stirring until cohesive dough forms, about 2-3 minutes.

Remove from heat and let cool for 5 minutes. Add eggs one at a time, mixing well after each until smooth and glossy.

Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper. Pipe 4-inch logs onto the sheet and bake for 30-35 minutes until golden brown.

While the choux cools, whisk together egg yolks, granulated sugar, cornstarch, and instant espresso powder. Warm whole milk in a saucepan, then gradually whisk into egg mixture. Return to saucepan and cook over medium heat until thickened, about 5-7 minutes.

Remove from heat, mix in unsalted butter and vanilla extract until smooth. Allow to cool completely. Make a hole at the bottom of each éclair and fill with pastry cream.

Combine powdered sugar, instant espresso powder, and brewed coffee until smooth. Dip the top of each éclair into the glaze, allowing excess to drip off. Place on a wire rack to set.