PREHEAT oven to 375°F. Mix 1 cup of the sugar, tapioca and cinnamon in large saucepan. Gradually add water. Stir in walnuts. Bring to full boil on medium heat, stirring constantly. Remove from heat; stir in apples. Pour into 8-inch square baking dish.
MIX remaining 1/3 cup sugar, flour, baking powder and salt in medium bowl; stir in cheese. Mix butter and milk. Add to flour mixture; stir just until moistened. Spoon over apple mixture.
BAKE 35 to 40 minutes or until golden brown. Cool. Top each serving with 1/4 cup of the ice cream.