Add the almond extract. In another bowl, sift together the flour, baking soda, and salt. With a wooden spoon, gradually stir the flour mixture into the shortening. The dough should be fairly firm. Wrap in waxed paper and refrigerate for 4 hours.
Place cookies on an ungreased cookie sheet.
Top each cookie with an almond half. Brush cookies lightly with beaten egg. Bake for about 10 minutes, or until light golden brown.