Wash and core the apples, leaving the bottoms intact. In a bowl, combine the walnuts, brown sugar, cinnamon, nutmeg, and 2 tablespoons of the maple syrup. Stuff the hollowedout center of each apple with the nut mixture.
Place the apples upright and close together in the pan. Combine the apple juice with the remaining 2 tablespoons of maple syrup and pour around the apples. Cover the baking pan with aluminum foil and bake for about 45 minutes, until the apples are tender.
Serve hot or cold with vanilla frozen yogurt or whipped cream