Place flour, salt, baking powder, and sugar in a mixing bowl and sift to thoroughly mix. Now rub shortening into the prepared flour and then mix to a dough with one-half cup of ice-cold water. Roll the pastry on a slightly floured pastry board one-fourth inch thick; cut in oblongs three inches wide and six inches long. Peel the banana and lay on the pastry; sprinkle with brown sugar, nutmeg, cinnamon, and butter. Brush the edges of the pastry with cold water and press firmly together, inclosing the banana. Lay on a well-greased and floured baking sheet, placing the side which was fastened together down. Brush with beaten egg and bake in a moderate oven for eighteen minutes. Serve just as you would other pastries.