Clean, peel and chop the pumpkin into pieces. Put it in a tray, sprinkle with the sugar, pour in the water and bake at 392°F (200 °C) for 30-40 min. until softened. Once ready, take it out and let it cool.
Whip the eggs with the sugar and vanilla. Pour the oil in lots. Sift the flour with baking powder in a bowl.
Pour in 1/2 the warm (not hot) water. Beat and pour in 1/2 the sugar, stir again, pour in the remaining water and flour. Stir until all the products are absorbed and you get a thick homogeneous mixture.
Pour 1 cup of the mixture into a bowl.
Mash or blend the pumpkin and put it in the bowl with the mixture. Stir until homogeneous.
Mix the rest of the cake mixture with the sifted cocoa and stir.
Smear a round tray, no larger than 10″ (26 cm) in diameter, with a little oil. Pour in the cocoa mixture, even it out and distribute the pumpkin mixture on top in several spots.
With a spoon, carefully press the pumpkin mixture downward, without spreading it out or mixing with the cocoa one.
Preheat the oven to 338°F (170 °C) and place the tray inside. Bake the cake to a dry toothpick for 30-40 min.