Smear a 12″ (30 cm) diameter oven dish with a little butter, place a phyllo pastry sheet, cover the bottom and walls with it but leave the edges to spill out. Put small, thin pieces of butter here and there, place another phyllo pastry sheet on top, sprinkle with a little pumpkin, sugar, cinnamon and walnuts.
Cover with another phyllo pastry sheet, place a little more butter, then another sheet and continue in this order - sprinkle with pumpkin, sugar, cinnamon and walnuts. Make 5-6 layers, with each layer consisting of 2 phyllo pastry sheets - one with the butter and covered with the other, with stuffing on top.
For the top, fold in the phyllo pastry sheets that spill out, place thin pieces of butter again here and there.
In a bowl, beat the eggs with the vanilla and milk. Cut the phyllo pastry into pieces, pour the mixture over them - use a spoon initially to pour it everywhere, then pour the rest into the cuts as well.
Put the phyllo pastry in the oven, heat it to 320°F (160 °C) and bake about 1 hour until it reddens nicely. Take it out and cool it, sprinkle with powdered sugar and serve.