Soak apples in water overnight. Next day, place ham in simmering water and cook further until soft. Add apples and brown sugar. Cook for 1 hour. For dumpling, beat the egg, butter and milk. Sift dry ingredients and add to mixture. Use milk to stiff batter.
Drop dumpling dough by spoonful into boiling ham and apples. Cover tightly for 15 minutes. Serve immediately.