Preheat oven to 450 degrees F. For dumplings: Mix together dry ingredients. Cut solid shortening into dry ingredients, make a well in the center, and add milk. Stir just until dough is fairly free from sides of bowl. Turn onto lightly floured board and knead 8 to 10 times. Cover and chill while preparing apples.
For apples: Combine sugar, butter, salt, and cinnamon and fill apple core hollows with this mixture, reserving some to sprinkle on top. Roll out dough to ¼ inch thick and cut into 4 squares. Place an apple onto each square and spread remaining sugar mixture over apples. Bring up corners of dough to cover apple and press edges together (dampen with a little water if necessary). Make sure edges are sealed or dumplings will pop open during baking. Brush with egg white and prick tops of dumplings with a fork. Carefully transfer dumplings to a baking pan. Bake for 10 minutes, then reduce heat to 350 degrees F and continue baking for about 40 minutes longer, or until apples are tender when tested with a wooden pick. Serve with cream.