Pour milk into a large saucepan, and bring to a boil over medium heat.
In a medium bowl, whisk together farina and one cup sugar and stir into boiling milk gradually. Stir continuously until mixture thickens (full boil), then remove from heat.
In a bowl, beat eggs with electric mixer on high. Add 1/2 cup sugar, and whip until thick, about 10 minutes. Stir in vanilla.
Add whipped eggs into farina mixture and set aside.
Grease 9x13 inch baking dish and layer five sheets of phyllo into pan, brushing each sheet of phyllo with butter.
Pour the mixture into the pan over the phyllo.
Cover with five sheets of phyllo, brushing each sheet with butter again.
Bake for 45 minutes until the crust is crisp and the custard has set.
To make syrup: in a small saucepan, stir together cup of sugar and water and bring to a boil.
When the Galaktoboureko comes out of the oven, spoon the hot sugar syrup over the entire area. Powder lightly with cinnamon.