In a bowl, beat the eggs. Add the sugar and continue beating. Pour in the oil, the flour sifted with baking powder and the walnuts. Stir well and add the finely chopped pumpkin (I used a hand blender with a grating accessory).
Add the cinnamon and stir carefully until well absorbed. Put 1/3 of the sheets in an 11″ (28 cm) form, while smearing between them with melted butter.
Pour on 1/2 the filling. Cover with another 1/3 of the sheets. Pour on the rest of the filling and cover with the rest of the sheets. Sprinkle with butter and bake at 356°F (180 °C) for 40 min. Take them out and leave to cool completely.
Boil a syrup from the sugar, water and vanilla. Boil 10 min. and leave it to cool slightly. Cut the cake carefully into pieces and pour the syrup over it. Leave it to cool and let sit for at least 4 hours before consumption.