Preheat your oven 180 deg C and prepare a 27 cm round shallow baking dish. Rub liberally with butter and sprinkle a few tablespoons of semolina flour to coat the base and sides of the dish. (see note 1)
In a large bowl combine the semolina, corn flour, eggs, lemon zest and vanilla. Whisk thoroughly to combine and set aside.
Heat the milk and sugar on medium heat. Be careful not to let the milk boil rapidly — allow it to come to a gentle simmer. (see note 2)
Slowly add one ladle of the milk to the semolina mixture and whisk until well combined. Repeat this step 2 more times and pour the tempered mixture back into the milk. Stir and allow the custard to thicken (this can take up to 5 mins), add the butter and whisk again. Pour the custard into the prepared baking dish.
For the topping combine the egg, sugar and milk in a ramekin and whisk well. Pour over the galatopita and brush, ensuring it covers the whole pie.
Bake in the oven for 45-50 mins. The galatopita is ready when it is puffed, and a skewer comes out clean. Allow the pie to rest and cool completely before serving. When serving, it's best to top each slice with a sprinkling of cinnamon and icing sugar. (see note 3)