First, adjust the oven rack so that it’s in the top third of the oven.
Have ready an ungreased or parchment lined baking sheet.
Mix together the flour, baking soda and salt, then mix in the nutmeg and orange zest. Add the oats and nuts and stir until thoroughly blended. Set aside.
In a mixing bowl, beat the softened butter until creamy, then add the brown sugar, egg white and vanilla and continue beating until creamy and light.
Add the flour mixture to the butter mixture and stir by hand until well blended, then add the banana and stir until blended.
Drop batter by heaping tablespoons onto ungreased baking sheet and bake cookies 12 minutes at 375, turning tray after the first 7 minutes.
Let cool slightly, then remove from tray and cool on a wire rack. When cool, mix together orange juice and confectioners’ sugar and drizzle over cookies.