Preheat your oven to 170° C (338° F) Fan.
Place a pot over medium heat and add 200ml of water, 200g of granulated sugar, lemon juice from ½ lemon, and 1 cinnamon stick. Bring to a boil and cook for 5 minutes. Remove from heat and let it cool.
Pull apart 300g of kataifi phyllo with your hands, transfer to a bowl, and add 150g of melted butter. Mix thoroughly to coat.
Line a 20 cm (8-inch) round baking pan with parchment paper, adding two more sheets in a criss-cross manner. This will help you unmold the pie.
Spread most of the buttered kataifi on the bottom and sides of the pan and refrigerate for 1 hour.
In a deep pot, heat 800ml of full fat milk and 100g of granulated sugar over medium heat.
In a bowl, mix the remaining 100g of granulated sugar, 2 medium eggs, 140g of fine semolina, and 1 teaspoon of vanilla extract. Beat until pale.
Gradually add the hot milk to the egg mixture while whisking continuously to prevent curdling. Pour it back into the pot and whisk until thickened.
Pour the custard over the kataifi in the pan and cover with the reserved kataifi. Press down gently to seal.
Bake for 1 hour and 10 minutes, until golden brown and crispy.
After baking, pour the cooled syrup over the pie immediately. Allow it to cool completely before unmolding.