Put the pumpkin pulp cut into pieces and the oil in a non-stick pan, and allow the pumpkin to cook with the lid on, until it becomes so soft that it can be crushed with a fork.
Add the chili pepper and garlic to the pan and sauté the seasoned pumpkin again for about ten minutes. Once this is done, add the salt and vinegar, and cook the pumpkin for a quarter of an hour, until a thick, compact, non-liquid consistency is obtained.
Finally, add the caraway to the pan with the pumpkin puree, stirring well.
Turn off the heat, transfer the pumpkin tershi into a bowl and allow it to cool.