Preheat the oven to 350°F (175°C). Butter a 9x13-inch baking dish and set aside.
Gently heat the Whole Milk with the Lemon Peel and the Cinnamon Stick in a saucepan until just below a simmer; remove from heat and let steep for 10 minutes, then strain and discard the peel and stick.
In a large bowl whisk together the Fine Semolina, Granulated Sugar, and Fine Salt. Add the Large Eggs and whisk until smooth.
Slowly temper the egg-semolina mixture by whisking in the warm milk a little at a time until fully combined, then return the mixture to the saucepan and cook over medium-low heat, stirring constantly, until it thickens to a smooth, spoon-coating custard (about 5–8 minutes).
Remove from heat and stir in the Unsalted Butter, the Lemon Zest, and the Vanilla Extract until the butter is melted and the custard is glossy. Let the custard cool slightly while you prepare the phyllo.
Unroll the Phyllo Pastry and keep it covered with a damp towel so it doesn't dry out. Brush one sheet lightly with melted butter and layer it in the prepared pan, repeating 6–8 sheets for the bottom layer to form a sturdy base.
Pour the warm custard into the buttered phyllo base and spread it evenly. Top the custard with another 6–8 sheets of butter-brushed phyllo, tucking and trimming the edges. Brush the top thoroughly with more melted butter.
Score the top phyllo into portions with a sharp knife to make cutting easier after baking. Bake until the phyllo is deep golden and crisp, about 40–50 minutes.
While the galaktoboureko bakes, make the syrup: combine Water, Granulated Sugar (if remaining in your measurements), the Lemon Peel (or a fresh piece), and the Cinnamon Stick in a small saucepan. Bring to a boil, then reduce heat and simmer for 8–10 minutes until slightly thickened. Remove from heat and stir in the Lemon Juice. Let the syrup cool until warm (not scalding).
When the pastry is out of the oven and still hot, pour the warm syrup evenly over the surface so it soaks into the layers. Allow the galaktoboureko to cool and rest for at least 2 hours (overnight is ideal) so the syrup and custard set together.
Cut through the scored lines into squares or diamonds and serve at room temperature. Store any leftovers refrigerated and bring to room temperature before serving for best texture.
