Prepare egg whites. Roughly dice almond paste. Top and tail figs, then finely chop. Wash orange and grate peel.
Make the cookie dough. Place almond paste, granulated sugar and confectioners' sugar in a food processor. Pulse until fine crumbs form. Add apricot preserves and 1 egg white at a time, pulsing after each addition to combine. Transfer almond mixture to a large bowl. Fold in figs and orange peel. Dough will be sticky.
Sugar coat the dough. Place the sugars for the coatings in separate shallow bowls. Drop tablespoons of dough into granulated sugar. Gently roll to coat and shape into 1¼" balls. Repeat in confectioners' sugar. Place 1" apart on parchment-lined baking sheets. Gently press down on each dough ball to slightly flatten the tops.
Bake 24-28 minutes or until tops are cracked and bottoms are golden brown. Transfer to wire racks to cool