Prepare the baking dish. Rub liberally with butter and sprinkle a few tablespoons of semolina flour to coat the base and sides of the dish.
In a large bowl, combine the semolina, corn flour, eggs, lemon zest and vanilla. Whisk thoroughly to combine and set aside.
In a large pot, 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.
Slowly add one ladle of the milk to the semolina mixture and whisk until well combined. Repeat this step 2 more times.
Pour the tempered mixture back into the milk. Stir and allow the custard mixture to thicken (this can take up to 5 mins), add the butter and whisk again.
Combine the egg, sugar, and milk in a ramekin and whisk well for the topping.
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, golden brown and a skewer comes out clean. Allow the pie to rest and cool completely before serving.
Milopita (Greek Apple Cake)
Portokalopita (Greek Orange Phyllo Cake)