Preheat the oven to 350°F (no fan). Line a 9x13-inch baking pan with parchment (no need to grease) and set aside.
Make the choux dough: combine butter, water, milk, salt and 2 teaspoons sugar in a medium saucepan. Heat over medium until the mixture just comes to a simmer and the butter is melted; do not boil.
Remove the pan from heat and add the flour all at once. Stir vigorously with a wooden spoon until a smooth ball forms. Return to low heat and stir constantly 2–4 minutes until the dough leaves a thin film on the pan bottom and feels slightly drier.
Transfer the dough to a mixing bowl and let cool 1–2 minutes. Beat in the eggs one at a time (stand mixer paddle or whisk by hand), waiting for each to incorporate fully. The finished dough should be glossy and fall from the spatula in a thick V — pipeable but not runny. If needed, add an extra beaten egg a little at a time.
Spread the choux dough evenly into the prepared pan with an offset spatula, smoothing the top. Bake for 33–35 minutes until puffed and deep golden. When it comes out of the oven, gently press any high domes flat with a clean kitchen towel to create an even sheet. Let cool completely.
While the choux bakes, make the pastry cream. Whisk the yolks and 1/2 cup sugar together until lighter in color. Stir the cornstarch and 3 tablespoons flour into the yolks until smooth.
Heat 2 cups milk in a saucepan until it begins to steam (do not boil). Slowly temper the hot milk into the yolk mixture while whisking constantly. Return everything to the pan and cook over medium, whisking, until it thickens and comes to a gentle boil; continue 30–60 seconds while whisking to fully activate the starches.
Remove from heat, whisk in the softened butter, vanilla and lemon zest until smooth. If you see any lumps, strain the cream through a fine sieve. Cover with plastic pressed to the surface and cool to lukewarm, then refrigerate briefly while finishing the rest.
Whip the cream for the top layer: place the very cold heavy cream and sifted powdered sugar in a chilled bowl. Whip with a hand mixer to soft-medium peaks (about 2–3 minutes). Keep refrigerated until assembly.
Assemble the cake: spread the cooled pastry cream evenly over the choux sheet. Chill 10–15 minutes to set slightly, then spoon or spread the whipped cream over the pastry cream in an even layer. Return to the fridge while you make the glaze.
For the glaze, heat 1/4 cup heavy cream until just simmering and pour over the chopped chocolate. Let sit 1 minute, then stir until smooth. Cool until slightly thickened but still pourable (warm to the touch).
Pour the glaze over the chilled cake and spread quickly for an even finish. Chill the cake at least 20–30 minutes before slicing into 12 squares. Serve chilled or at cool room temperature.
Store leftovers tightly covered in the refrigerator for up to 2 days; the layers will soften over time.