Preheat your oven to 200°C (about 400°F). In a medium saucepan over medium heat, combine milk, water, unsalted butter, salt, and sugar. Stir until the mixture comes to a gentle boil. Remove from heat and quickly stir in the flour until fully incorporated.
Allow the mixture to cool slightly before adding eggs one at a time. Mix well after each addition until the batter is smooth and glossy.
Divide the choux pastry into two equal portions and spread each portion onto parchment-lined baking sheets in rectangular shapes. Bake for about 25–30 minutes until golden brown and puffed up.
In another saucepan, combine milk with sugar over medium heat until warm but not boiling. In a separate bowl, whisk together eggs and cornstarch until smooth. Gradually add some warm milk mixture while whisking continuously. Pour everything back into the saucepan while whisking constantly until thickened over low heat.
Once thickened, remove from heat and stir in vanilla extract and room temperature unsalted butter until well blended. Allow the filling to cool completely.
To assemble, place one layer of baked choux pastry on a serving platter. Spread half of your cooled cream filling evenly on top before placing the second layer over it. Dust powdered sugar generously over the top layer.