Preheat the oven to 400 degrees F (200 degrees C).

Sift flour, salt, cinnamon, baking soda, and nutmeg together into a bowl.

Beat sugar and shortening together in a separate large bowl with an electric mixer until light and fluffy. Add oatmeal, banana, nuts, and egg; beat well. Add in flour mixture; mix well.

Drop teaspoonfuls of dough onto ungreased cookie sheets.

Bake in the preheated oven until edges turn lightly brown, about 15 minutes. Cool on a wire rack. Store in an airtight container.