Heat oven to 350°F. Grease and flour 13 x 9 x 2-inch metal baking pan.
Stir together flour, salt and baking soda in a medium-size bowl until well blended.
Beat together sugar and butter in large bowl on medium-low speed until coarse crumbs form. Add eggs, applesauce, apple juice concentrate and ginger; mix on low speed just until eggs are beaten. Gradually beat in flour mixture just until blended. Stir in apple. Spread in prepared pan.
Bake in 350°F oven for 20 to 25 minutes or until a wooden pick inserted in center of cake comes out clean. Remove pan to wire rack and let cool completely.
Beat together powdered sugar, milk and pinch salt in small bowl until smooth and of good drizzling consistency. If too thick, add milk, a teaspoon at a time, until desired consistency. Pour into heavy-duty plastic food-storage bag; snip off very small tip from a corner. Drizzle glaze over top.