In a medium saucepan, combine the diced apples or peaches, granulated sugar, cinnamon, nutmeg, and lemon juice.

Cook over medium heat, stirring occasionally, until the fruit is tender and the mixture has thickened, about 10 minutes.

Dissolve the cornstarch in water and add it to the fruit mixture. Continue cooking for another 2 minutes until the filling is thick and glossy. Remove from heat and let it cool.

Roll out the pie crusts on a lightly floured surface and cut into 8 equal-sized circles (about 4–5 inches in diameter).

Place a spoonful of the cooled fruit filling in the center of each dough circle.

Fold the dough over the filling to create a half-moon shape. Press the edges together with a fork to seal.

Heat the vegetable oil in a large, deep saucepan or skillet to 350°F (175°C).

Carefully add the pies to the hot oil, a few at a time, and fry until golden brown, about 2–3 minutes per side.

Remove the pies from the oil and drain on paper towels.

Allow the pies to cool slightly before dusting with powdered sugar, if desired. Serve warm.