Use a butternut squash pumpkin, grate it finely. Grind the walnuts finely.
In a bowl, mix the pumpkin, sugar, walnuts and vanilla. Stir well.
Smear the sheets with a little oil 1 at a time. Place them together in pairs, to prevent burning during baking. Spread pumpkin filling on top of each pair evenly and roll it up into a roll.
Arrange the rolls in an oiled tray. Bake in a moderate oven. To prevent the phyllo pastry from burning before it's fully baked, cover it with foil during the initial 10 min. of baking.
Meanwhile, prepare the syrup. Put a pot with the water and sugar on the stove and leave to come to a boil. Then leave the syrup to cool.
Once the phyllo pastry is ready, pour the syrup over it and cover it to smother. Leave it for at least 3 hours to take in the syrup.