Cook apples in water for 20 minutes. Combine sugar, cinnamon, and cornstarch. Add to apples. Add lemon juice. Cook until thickened. Cool.
Cut shortening into flour. Combine egg, water, salt, and vinegar. Pour into flour mixture, and mix.
Pinch small amount of dough, and roll out on floured board.
Cut out circles, using a 5-inch saucer as a guide. Put 1 tablespoon apple mixture on dough. Wet edges of dough with iced water. Fold dough over apple mixture, and seal by pressing a floured fork around edges. Fry in 1–2 inches of oil in a skillet on medium-high setting. Cook until golden brown, turning only once. Glaze with a mixture of powdered sugar and water.
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