Combine 1 cup of water and 1/2 cup of butter in a saucepan over medium heat. Bring it to a boil, then remove from heat and stir in 1 cup of all-purpose flour until a smooth ball forms.

Allow the mixture to cool for about 10 minutes before adding in 4 room temperature eggs, one at a time, mixing thoroughly until the dough is glossy and smooth.

Preheat your oven to 400°F (200°C). Line two baking sheets with parchment paper. Divide the choux pastry into two equal portions and spread each half onto the prepared sheets, smoothing them into even rectangles.

Bake for 25-30 minutes, or until the pastry layers are golden brown and puffed up. Remove them from the oven and let cool completely.

In a medium saucepan over medium heat, whisk together 2 cups of milk, 1/2 cup of sugar, 1/4 cup of cornstarch, and 4 eggs. Stir constantly until thickened, about 8-10 minutes.

Once thickened, remove from heat and stir in 1 tablespoon of vanilla extract. Allow the custard filling to cool slightly.

Place one cooled pastry layer on a serving platter. Spread the custard filling evenly across the surface. Place the second pastry layer on top, pressing gently.

Cover the assembled cake with plastic wrap and refrigerate for at least 2-3 hours, or overnight if possible.