Put the sugar, water, lemon peel strips, and cinnamon stick in a 2-quart / 1.9 L saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves, then simmer for 8 minutes, until the syrup lightly coats the back of a spoon. Stir in the lemon juice and set it aside to cool completely. It needs to be cool when the pie comes out of the oven.

Whisk the milk, sugar, and salt in a 4-quart / 3.8 L heavy-bottomed saucepan over medium heat for about 5 minutes, until steaming but not boiling. Slowly rain in the semolina while whisking. Cook for 5 to 7 minutes, whisking constantly, until the custard is as thick as pudding and the whisk leaves trails.

Take the pan off the heat and whisk in the butter, vanilla, and lemon zest. Beat the eggs in a large bowl, then whisk in one ladle of the hot custard to warm them. Pour the egg mixture back into the pan and whisk until smooth. Press plastic wrap onto the surface so no skin forms, and let it stand while you prep the phyllo.

Heat the oven to 180 C / 350 F. Brush a 23 x 33 cm / 9 x 13 inch baking dish with melted butter. Unroll the phyllo and keep it under a damp kitchen towel. Lay in 10 sheets one at a time, brushing each with melted butter and trimming or folding the edges to fit.

Pour the custard over the phyllo and smooth the top. Layer the remaining 10 sheets over it, brushing each with butter. Tuck the edges down, brush the top with the last of the butter, and cut through the top 5 or 6 sheets into 12 squares with a sharp knife.

Bake for 45 minutes, until the top is deep golden and the center only jiggles slightly when you nudge the dish. If the top browns before the center sets, tent it loosely with foil.

Pour the cooled syrup slowly over the hot pie as soon as it comes out of the oven. You'll hear it sizzle, and that's normal. Let the pie cool at room temperature for 1 hour, then chill it, loosely covered, for at least 2 more hours.

Cut along the scored lines with a gentle sawing motion. Don't cut before the 3 hours are up, or the custard will run and the bottom layers will turn soggy. Serve cool or at room temperature.