Cut apple in half and remove core. Cut each half into slices approximately ⅛-inch thick.
Stir together brown sugar and water in medium saucepan. Add apple slices. Cook, stirring gently over medium heat, until apple slices are softened, about 5 minutes.
Sprinkle cranberries in bottom of nonstick or greased 9-inch cake pan. Arrange apple slices over cranberries, drizzling with brown sugar sauce. Set aside.
In large bowl or mixer, beat butter with granulated sugar until thoroughly combined. Add applesauce and egg.
In separate bowl, mix together flour, baking soda, and cinnamon. Gently blend into applesauce mixture.
Spoon batter over apples and cranberries, spreading evenly.
Bake 30 minutes, or until toothpick inserted into center comes out clean.
Remove from oven and cool 15 minutes before turning cake out onto wire rack to cool completely.
