Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a large bowl, cream together the shortening and white sugar until smooth. Beat in the eggs one at a time. Stir in the vanilla and pumpkin until well blended. Combine the flour, baking soda, baking powder, salt, cinnamon and nutmeg; stir into the pumpkin mixture. Mix in the chocolate chips. Stir in the walnuts if desired. Drop by teaspoonfuls onto the prepared cookie sheets.
Bake for 12 to 15 minutes in the preheated oven, until edges begin to brown. Allow to cool for a few minutes on the baking sheets before removing to wire racks to cool completely.