Cook the pumpkin until it is soft, then mash it until smooth. Set aside.
In a large saucepan, combine the coconut milk, brown sugar, water, vanilla extract, ground cinnamon, ground nutmeg, and a pinch of salt.
Heat the mixture over medium heat, stirring constantly, until the sugar is dissolved and the mixture is well combined.
In a small bowl, mix the cornstarch with a little water to form a smooth paste.
Gradually add the cornstarch paste to the coconut milk mixture, stirring constantly to prevent lumps from forming.
Continue to cook the mixture, stirring frequently, until it thickens to a pudding-like consistency.
Stir in the mashed pumpkin until it is fully incorporated into the coconut milk mixture.
Cook for an additional 2-3 minutes, stirring constantly, until the mixture is smooth and well combined.
Remove the fekei from the heat and let it cool slightly.
Pour the fekei into serving bowls or a large serving dish.
Enjoy your meal!