Cream shortening; add brown sugar, beating well. Add eggs and banana; beat well.
Sift together flour, baking powder, baking soda, salt, and spices. Add to creamed mixture; mix well. Stir in pecans.
Drop dough by rounded tablespoonfuls, 2 inches apart onto greased cookies sheets. Bake for 12 minutes. Remove to wire racks to cool. Dip half of cooled cookies into Powdered Sugar Icing.
To Make Icing: Combine 3 cups confectioner's sugar, 1 tablespoon melted butter or margarine, and 3/4 teaspoon vanilla extract. Add milk to yield desired consistency (you may need to add a little extra), beating until smooth.