Start by cooking the chestnuts. Lay the chestnuts on their flatter side and cut or score halfway around the outer shell until you reach the flesh of the nut. Place them in a pressure cooker, cover with water, and cook for 10 minutes.

Turn off the heat and, as soon as you can handle them without getting burnt, start peeling the chestnuts one by one (do this while still hot or they will be hard to peel). Leave the remaining chestnuts in their cooking liquid while peeling them. Remove both the outer and inner skins, then set aside.

Put the brown sugar, water, and vanilla extract in a pot and bring to a boil. Add the peeled chestnuts and roughly crush them with a wooden spoon. Cook for a couple of minutes, then turn off the heat. Blend until completely smooth.