In a large mixing bowl, beat the butter, brown sugar, and applesauce until smooth. Add the egg and dark molasses, mixing well.
In another large bowl, combine the all-purpose flour, baking soda, ground ginger, ground cinnamon, allspice, and ground cloves. Whisk together.
Gradually add the dry mixture to the wet mixture, stirring well. Use your hands to form a large ball, the dough will be a little sticky.
Wrap the dough in plastic wrap and chill in the refrigerator for at least 2 hours.
Preheat the oven to 350°F. Dust your working area with flour, and roll out the dough to 1/8-inch thickness.
Cut the dough into triangles to resemble trees, and place them on a silpat-lined baking sheet.
Bake for 10 to 12 minutes until firm to the touch. Let cool.
Prepare the icing by mixing the egg whites with lemon juice and then combining with powdered sugar. Add green food coloring as desired.
Once cooled, decorate the cookies with the icing and add the sprinkles.
Let the icing set before serving or storing.