Warm the milk and lemon peel in a saucepan. Stir in semolina with a wooden spoon until the mixture is thoroughly blended and thickened. In a mixing bowl, beat the eggs, sugar, and vanilla until light and add to the pan, stirring over medium-low heat until it reaches a creamy custard consistency. Remove from heat, take out and discard lemon peel, and allow to cool completely. Stir occasionally to keep the custard from forming a skin on top.
Preheat oven to 180°C.
Lightly brush a baking pan (33 x 23 x 5 cm or equivalent) with butter. Line the bottom of the pan with 8 sheets of phyllo, brushing each sheet well with the melted butter. Add the custard filling. Fold the excess phyllo that overlaps the pan in over the custard. Top with the remaining phyllo, brushing each with butter. Use a scissors to trim the top sheets to the size of the pan. Spray the top lightly with water and bake at 180°C for 30-40 minutes, until the top is golden brown.
Remove from oven, sprinkle with icing sugar and cinnamon while hot, and serve warm.
Serving tip: In Greece, bougatsa is cut with a pizza cutter.