Remove skin and fat from outside of smoked pork. Place pork in a Dutch oven; add enough water to cover meat. Bring water to boiling; reduce heat. Cover and simmer for 30 minutes. Stir in dried apples and brown sugar. Cover; simmer 1 hour more.
Meanwhile, for dumplings, in a bowl stir together flour, baking powder, and salt. In a small bowl combine egg, milk, and melted margarine or butter. Add to flour mixture; stir with a fork just until combined. Drop dough by rounded tablespoonfuls in 10 mounds atop the simmering liquid. Cover; simmer for 20 minutes (do not lift the cover) or until a toothpick inserted into the dumplings comes out clean.
Serve pork on a platter with the dumplings and apples. Spoon a small amount of the remaining liquid over the meat. Makes 8 to 10 servings.