Preheat oven to 350 degrees F (175 degrees C). Grease and flour two 9x5-inch loaf pans.
Combine flour, ground ginger, cinnamon, cloves, and salt in a bowl.
Cream sugar and butter in a large bowl with an electric blender until light and fluffy; stir in 1 teaspoon orange extract. Mix baking soda into applesauce and stir into butter mixture. Add flour mixture and mix until batter is smooth. Pour batter into the prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into center of a loaf comes out clean, 40 to 50 minutes. Remove from pan and cool on a wire rack until cool, about 1 hour.
Combine cream cheese, vanilla extract, and 1/2 teaspoon orange extract in a bowl; beat with an electric mixer until well combined. Beat in confectioners' sugar gradually. Spread frosting over cooled loaves. Decorate with crystallized ginger.