Preheat oven to 400 degrees F. In a 4- to 6-quart Dutch oven combine apple slices, brown sugar, balsamic vinegar, and cinnamon. Bring to boiling, stirring occasionally once apples begin to release their juices; reduce heat. Simmer, covered, about 5 minutes or until apples are nearly tender, stirring occasionally. In a small bowl stir together the cold water and cornstarch; add to apple mixture. Cook and stir until thickened and bubbly. Keep hot over low heat.
In a large bowl combine flour, ground nuts, granulated sugar, baking powder, and salt. Using a pastry blender, cut in butter until pieces are pea size. In a medium bowl stir together eggs, milk, and cheese. Add cheese mixture to flour mixture; stir just until combined. Spoon hot apple mixture evenly into a 3-quart rectangular baking dish. Using a spoon, drop dough mixture into 12 mounds on top of fruit.
Bake in the preheated oven for 25 to 30 minutes or until top is golden and filling is bubbly. Cool on a wire rack for 30 minutes. Serve warm. If desired, serve with ice cream.