Adjust oven rack to lower third of oven. Preheat oven to 350 degrees F. In a 12-inch cast iron or oven-going skillet, melt 1/4 cup butter. Stir in maple syrup and ginger. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes, stirring occasionally. Set aside.
Core apples; peel if desired. Cut into 1/4-inch-thick slices. Arrange apple slices and dried cherries in the skillet, turning apples to coat with syrup mixture. In a small bowl, combine flour, baking powder, salt, apple pie spice, and baking soda; set aside.
In a large bowl, beat 1/4 cup softened butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar and egg yolks; beat until combined. Alternately add flour mixture and milk to butter mixture, beating on low speed after each addition just until combined.
Wash beaters thoroughly. In a medium bowl, beat egg whites on medium speed until soft peaks form (tips curl). Gradually add granulated sugar, beating on high speed until stiff peaks form (tips stand straight). Fold one-third of the beaten egg whites into batter to lighten. Gently fold in the remaining beaten egg whites. Pour batter evenly over apple slices and dried cherries in skillet, being careful not to disturb apples and cherries.
Bake for 25 to 35 minutes or until a toothpick inserted near the center comes out clean. Cool in skillet on a wire rack for 5 minutes. Using a sharp knife or narrow metal spatula, loosen edge of cake from side of skillet. Carefully invert onto a serving plate. Serve warm cake with ice cream. Makes 8 to 10 servings.