Heat water, milk, butter, sugar, and salt in a saucepan over medium heat until the butter melts and the mixture just simmers.
Remove from heat, add sifted flour all at once, and stir vigorously until a dough forms and pulls from the sides.
Return to medium heat and cook the dough, stirring, for 2 to 3 minutes until a thin film coats the pan.
Transfer the dough to a mixer bowl and beat on low for 1 minute to cool slightly.
Add eggs one at a time, beating well after each, until the batter is glossy and forms a V-shaped ribbon from the paddle.
Pipe 4 to 5 inch logs onto parchment-lined sheets using a large round tip, spacing 2 inches apart.
Brush lightly with beaten egg and smooth any peaks with a damp finger.
Bake at 400°F/205°C for 15 minutes, then reduce to 350°F/175°C and bake 15 to 18 minutes more until deeply golden and puffed.
Turn off the oven, prop the door open, and let eclairs dry for 10 minutes before cooling on a rack.
For pastry cream, heat milk to steaming; whisk sugar, cornstarch, yolks, and 1 teaspoon vanilla until smooth, then temper with hot milk.
Return to the saucepan and cook over medium heat, whisking, until thick bubbles appear and the cream is glossy.
Remove from heat, whisk in butter, strain through a sieve, press plastic wrap on the surface, and chill until cold.
Whip cold heavy cream to soft peaks and fold into chilled pastry cream to make vanilla diplomat cream.
Fold in half of the diced strawberries and the remaining 1 teaspoon vanilla to the cream.
Poke two small holes in the bottom of each éclair shell and fill with the strawberry-vanilla cream using a small round tip.
Warm strawberry jam until loose, strain if needed, cool slightly, and spread a thin layer on top of each filled éclair.
Make glaze by melting white chocolate with 30 ml cream until smooth and spreadable.
Dip or spread the white chocolate glaze over the jam-topped eclairs and set on a rack.
Sprinkle crushed freeze-dried strawberries over the glaze and garnish each with a fresh strawberry slice.
Chill eclairs for at least 1 hour to set before serving and dust lightly with powdered sugar.