In a saucepan, combine butter, water, and a pinch of salt. Bring to a boil, then quickly stir in the flour until a dough forms and pulls away from the pan.

Remove the saucepan from heat and let the mixture cool slightly. Add eggs one at a time, mixing thoroughly after each addition until smooth.

Spread the choux dough evenly on two parchment-lined baking sheets into rectangles. Bake at 400°F (200°C) for about 30 minutes, or until golden brown.

In another saucepan, mix milk, sugar, and cornstarch. Heat gently while whisking until thickened, then stir in vanilla extract. Let cool completely.

Place one choux pastry layer on a serving platter. Spread the custard filling evenly over it, and top with the second layer of choux.

Refrigerate the assembled cake for at least 2 hours to let the custard set. Slice and serve chilled.