1. Preheat oven to 375°F (190°C).

For the Custard Filling

1. In a large saucepan, heat the milk over medium-high heat until just before boiling. Lower the heat to medium-low and slowly whisk in the farina. Whisk the mixture until slightly thickened, about 10 minutes. Add the cinnamon stick and remove the pan from the heat.
2. In a large bowl, vigorously beat the eggs with granulated sugar until fluffy, about 5 minutes. To temper the egg mixture, whisk in a ladleful of the warm farina and milk mixture. Then pour the warmed egg and sugar mixture into the pan with the farina and milk mixture, continuing to whisk. Add the lemon zest and vanilla. Return the pan to the stove. With a wooden spoon, stir the cooking liquid over medium-low heat until it thickens, about 5 minutes. When the custard has thickened, remove from heat and stir in the vanilla extract and melted butter. Set aside and let cool slightly.

For the Phyllo Layers

1. Carefully remove the phyllo roll from the plastic sleeve. Keep the phyllo dough damp under a moist cloth throughout the process. Using a pastry brush, brush the bottom and sides of a 9 x 12-inch baking pan with melted butter. Carefully place a sheet of phyllo (you may have to trim the edges) on top. Brush a little butter over the dough and continue layering phyllo and brushed butter for 10-12 layers. To prevent drying, cover the dough with a damp dish towel while assembling the layers.
2. Pour the custard in an even layer on top of the sheets, smoothing the surface with a spatula. Add the remaining phyllo sheets on top, brushing each sheet with melted butter between layers. Before baking, gently score the top layer of phyllo into squares with a sharp knife to enable easier cutting of pieces later.
3. Bake for 45 minutes or until the top is golden brown.
4. While the Galaktoboureko is baking, prepare the syrup: Add the sugar, water, and lemon peel to a saucepan. Boil over medium-high heat for approximately 10–15 minutes. Remove the lemon peel and stir in the lemon juice. Remove from heat and set aside to cool.
5. When the Galaktoboureko is ready, let it cool for 10 minutes. Then, pour the syrup evenly over the entire phyllo surface. Allow the pie to absorb the syrup for at least 1 hour before serving.