It's important to weigh the nuts for accurate amounts, as volume can differ enormously. Extra cookies keep well, covered in plastic wrap and frozen.
Reprinted with permission from The Martha Stewart Living Cookbook by Martha Stewart Living Magazine, copyright © 2007. Published by Clarkson Potter, a division of Random House, Inc.
Heat the oven to 350 degrees. Line two baking sheets with parchment paper, and set aside.
In the bowl of a food processor, blend 3 ½ ounces almonds (about 1 cup) with 1 cup of sugar until almonds are finely ground. Transfer the almond mixture to a medium bowl. Stir in flour, orange zest, and crushed anise seeds.
Using an electric mixer, whisk the egg whites, salt, and remaining ¼ cup sugar to soft glossy peaks. Fold egg-white mixture into dry ingredients until just blended.
Spoon level tablespoons of batter 2 inches apart on prepared baking sheets. Using remaining ¾ ounce almonds, arrange 3 sliced almonds on each cookie. Sift confectioners' sugar over cookies. Bake until cookies are lightly browned along edges, about 12 minutes. Cool slightly before removing from sheets with a spatula.