Stir together fresh apples, brown sugar, lemon juice, and cinnamon in a small saucepan over high heat. Bring to a boil, stirring constantly. Boil until apples start to soften, about 8 minutes. Stir in dried apples and cool completely.

Meanwhile, let chilled dough stand for 30 minutes. Place a few layers of paper towels on a rack set over a baking sheet.

Lightly flour work surface and roll dough out to a 12x16-inch rectangle about 1/8-inch thick. Cut out twelve 4-inch rounds. Place 2 tablespoons apple mixture in the center of 1 round. Lift carefully. Fold round in half, keeping filling securely in center. Press edges together. Crimp edge thoroughly with a floured fork. Repeat with remaining filling and dough.

Heat 1 inch of oil to 350 degrees F (175 degrees C) in a 10-inch cast-iron skillet or other straight-sided deep, heavy skillet.

Slide pies into oil, 3 at a time. Fry, adjusting heat as needed to keep oil at 350 degrees F, and turning every 30 seconds to prevent scorching, until golden brown, blistered, and crispy, about 3 minutes. Drain on paper towels. Let cool a few minutes, then shower excessively with confectioners' sugar.