Make the poppy seed mixture: mix ground poppy seeds,granulated sugar and vanilla, pour hot milk and whisk until incorporated. Fold in lightly beaten egg whites. Set aside.
Make the cheese mixture: Mix eggs, sugar, vanilla and lemon zest. Fold in fresh cheese. Set aside.
Make the walnut mixture: Mix ground walnuts and sugar, pour hot milk and rum (if using) and whisk until incorporated. Set aside.
Make the apple filling: Mix all the ingredients. Set aside.
Preheat oven to 180 C (350 F). Grease 33x23 cm (13x9 inch) baking pan with butter.
Stack 3 sheets of phyllo dough and brush the 3rd with melted butter. Spread poppy seed filling over it, and smooth into an even layer. Spread two sheets of phyllo dough over poppy seed filling and brush with melted butter. Spread cheese mixture over it and smooth the top into and even layer. Stack 2 sheets of phyllo dough and brush with melted butter. Spread
walnut mixture and smooth the top into an even layer. Stack 2 sheets of phyllo dough and brush with melted butter. Using your hands squeeze liquid from apple filling and the spread it over the phyllo dough. Smooth the top and stack with three sheets of phyllo dough. Brush with melted butter.
Bake around 40 minutes, or until top sheet of phyllo dough is golden brown (depending on your oven, check it at 30 minutes). Leave it to cool a bit, dust with icing sugar, cut into squares and serve warm with glass of milk. It is delicious served cold, too.