Place squash in a medium pot, and add enough water to cover, plus two inches. Bring to a boil. Cover, lower heat, and simmer for 20 minutes or until very tender. Drain well.

Puree in a food processor or blender and let cool completely.

Place two cups of the squash puree in a large bowl. Add sugar, cinnamon, nutmeg, oil, vanilla and eggs. Mix well with a spoon.

In a separate, large bowl, sift flour, baking soda, and salt together and make a well in the center. Add the squash mixture to the center of the flour mixture and stir until smooth. Mix in walnuts.

Spoon batter into greased muffin pan cups and bake for 30–35 minutes or until golden and shrinking from sides of pan. Cool before serving.

Preheat oven to 350 degrees Fahrenheit.