Cream shortening in a large mixing bowl; gradually add sugar, beating well. Add eggs and banana; beat well.
Sift together flour, baking powder, soda, salt, cinnamon, and cloves in a small mixing bowl; add to creamed mixture, stirring well. Stir in pecans.
Drop dough by tablespoonfuls 2 inches apart onto greased cookie sheets. Bake at 350° for 12 minutes. Remove from cookie sheets, and cool on wire racks. Spread tops of cooled cookies with Powdered Sugar Icing.