For the syrup:
Place all the ingredients for the syrup in a saucepan, stir and bring to a boil. Let them simmer for approx. 5 min in medium heat.
Remove the half-lemons and let the mixture cool down.

For the cream:
Keep aside 1 cup of the total fresh milk and half the sugar. Heat the remaining milk and sugar, cinnamon and lemon zest in a saucepan, until it is warm and releases the lemon and cinnamon fragrances.
In a deep bowl, beat the 5 eggs and 2 yolks with a hand mixer for a few minutes, until they are fluffy and no longer smell of egg. Add the remaining sugar and keep beating for a few minutes until the sugar melts properly. Finally, add the vanillas.
Add to the mixture the semolina and the 1 cup of milk that you have kept aside.
Transfer some warm milk (2 cups) from the saucepan to the bowl with the egg mixture, stirring, until the eggs are warm and diluted. Empty all the mixture from the bowl into the saucepan with the warm milk and stir for a few minutes with an egg whisker or wooden ladle, until the cream thickens.
Once it thickens, remove it from the fire and add the butter, stirring until it melts, like it is strolling on the cream surface. Leave it aside to form a crust. Remove the cinnamon stick.
Leave the cream aside to cool down.
How to form the galaktoboureko in a baking pan
Heat 200 gr butter in a small saucepan (until it only melts without becoming too hot) and leave it to cool down a little, until just before it starts to thicken.
Butter a round baking pan (36 or 38 cm) or an oblong baking pan (38×28 cm). Layer 7 Filo Pastry Sheets radially, buttering each one, so that they reach well over the baking pan brim.
Pour the cream over the layered sheets. Roll the excess part of the sheets inwards over the cream, and layer the remaining 5 sheets on top, buttering each one.
With a soft ladle, tuck the sheets edges that reach over the baking pan under the galaktoboureko. Butter the surface again.
Carve the surface in pieces. Pour the remaining melted butter, so that it is absorbed through the carvings. Sprinkle the sheets with a little water on the surface, so that they don’t rise during baking.
Bake at 180°C with extra heat on the bottom rack, for approx. 1 hour, until golden brown.
Alternatively, bake the galaktoboureko in air, at 160°C, on the middle rack, for approx. 50 min, until golden brown.
Take the galaktoboureko out of the oven and gradually pour the cold syrup all over.
Leave the warm galaktoboureko to cool down and then cut in pieces to serve. If you cut it while still warm, its juices will pour out in the baking pan.
Alternatively, leave it aside to cool down and then pour over the warm syrup.