In a medium bowl, cream together shortening and sugar until light and fluffy. Beat in eggs one at a time. Stir in vanilla extract, baking powder, salt, and instant banana pudding mix. Mix in 2 cups flour. Gradually mix in remaining 1/2 cup flour as needed to form a workable dough. Cover, and chill in the refrigerator at least 2 hours.
Preheat oven to 375 degrees F (190 degrees C). Grease baking sheets. Shape dough into walnut sized balls, and place 2 inches apart on the prepared baking sheets. Flatten balls to a thickness of about 1/4 inch.
Bake 8 to 10 minutes in the preheated oven, or until lightly browned.