Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a large bowl, cream together the shortening and sugar until light and fluffy. Beat in the egg, then stir in the pumpkin and vanilla. Combine the flour, baking powder, baking soda, salt, nutmeg, and cinnamon; gradually mix into the creamed mixture. Stir in the walnuts and chocolate chips. Drop dough by teaspoonfuls onto the prepared cookie sheets.
Bake for 15 minutes in the preheated oven, or until light brown. Cool on wire racks.