Clean the pumpkin and cut it into pieces 1/2″ (1 cm) thick. Smear a tray with a little butter, arrange the pieces, sprinkle on 2 tbsp sugar, pour in the water and put it in a preheated 356°F (180 °C) oven for 30 min. until softened.
To make the caramel, use a ceramic or Teflon pan. Distribute the sugar into it, put it on the stove and melt it to a golden caramel. It's important not to stir the sugar, so it doesn't turn to lumps. Lift the pan carefully and swirl it until the sugar melts.
Pour the caramel into a round tray, no larger than 10″ (26 cm) in diameter. If you were to use a wider tray, the cream would end up flat, without the necessary height. Spread out the caramel all over the entire bottom, while carefully swirling and tilting the tray. Don't touch it, the caramel is extremely hot!
Take the ready pumpkin out and carefully transfer the pieces on top of the hot caramel. That way they'll stick and won't swim to the surface when you pour on the cream. Leave to cool.
Remove from the stove. In a bowl, whip the eggs and pour a little of the milk at a time in a thin trickle, while stirring nonstop, in order to even out the temperatures of the 2 mixtures and not curdle the eggs.
Once they're tempered, you can pour the egg mixture carefully into the milk, again while stirring nonstop. Pour the mixture through a strainer. Pour the resulting mixture carefully into the tray over the pumpkin and caramel.
Put it in the oven, turn it on to 320°F (160 °C) and bake for 1 hour until it firms up and gains a golden color. Take it out, cool and put in the fridge.