Preheat oven to 400°F. Boil first 3 ingredients in large skillet until reduced to 1 1/4 cups, about 12 minutes.
Meanwhile, cut cone-shaped piece from stem end of each apple, 2 inches wide at top and 1 inch deep. Using melon baller, core, leaving bottom intact. Turn apple on its side. Starting halfway down, make 1/4-inch-deep slit all around.
Mix mincemeat, walnuts, cherries, and crystallized ginger in small bowl; spoon into apples, mounding in center.
Arrange apples in 11x7x2-inch baking dish. Spoon cider mixture over and around.