To begin, preheat your oven to 350°F (175°C). In a medium saucepan over medium heat, combine milk, semolina, and sugar for the custard. Stir continuously to prevent lumps, cooking until the mixture thickens slightly, about 5-7 minutes.

In a separate bowl, whisk the eggs, lemon zest, and vanilla extract until smooth. Slowly add a ladle of the warm milk mixture to the eggs, whisking constantly to temper them. Gradually pour this mixture back into the saucepan, stirring continuously, and cook until thickened and creamy. Remove from heat, add the butter, and stir until smooth. Set aside to cool slightly.

To prepare the phyllo, lightly grease a baking dish (approximately 8x8 inches). Lay one sheet of phyllo at the bottom of the dish and brush with melted butter. Continue layering and buttering four sheets, ensuring each layer is evenly coated to prevent dryness and provide a crisp texture.

Once the bottom layers are ready, pour the warm custard into the prepared phyllo base, smoothing the top with a spatula. Ensure the custard is spread evenly to reach the edges for a balanced filling.

Layer the remaining four sheets of phyllo on top of the custard, buttering each layer generously. Tuck in any overhanging edges or trim them to fit neatly. Brush the top layer with additional butter to achieve a golden, crisp finish during baking.

Using a sharp knife, gently score the top layers of the phyllo into squares or diamonds, being careful not to cut into the custard. This will help create clean cuts once baked and prevent the phyllo from shattering.

Bake the Galaktoboureko in the preheated oven for 45-50 minutes, or until the phyllo is golden and crisp. While it bakes, prepare the syrup: combine sugar, water, honey, cinnamon stick, and lemon peel in a saucepan over medium heat. Bring to a boil, then simmer for 8-10 minutes until slightly thickened. Remove from heat and let cool.

When the Galaktoboureko is finished baking, pour the cooled syrup evenly over the hot pastry. Let it soak for 15-20 minutes before serving. Garnish each slice with a sprinkle of lemon zest, if desired, and enjoy warm for the most authentic experience.