1. Preheat the oven to 350° F. Gently warm the orange juice and rum in a saucepan over low heat. Remove the pan from the heat, add the figs, and let soften for 20 minutes.
2. Remove any stems or hard ends from the figs. Purée the figs with their soaking liquid in a food processor. Grind in the brown sugar, applesauce, yogurt, oil, and egg whites.
3. Sift the dry ingredients--2 cups flour, baking soda, baking powder, cinnamon, ginger, nutmeg, cardamom, cloves, and salt--into a mixing bowl. Fold in the wet ingredients and stir just to mix. Spoon the batter into two 9-inch loaf pans (preferably nonstick), sprayed with spray oil and lightly floured. Bake the breads for 50 minutes, or until an inserted skewer comes out clean. Let the breads cool for 10 minutes, then invert onto cake racks. Let cool completely before serving.