Melt the butter in a pan over medium heat. Add diced apples, granulated sugar, brown sugar, cinnamon, and a pinch of salt. Cook for about 6-8 minutes, stirring occasionally, until apples are tender.

Sprinkle flour over the softened apples and stir well. Cook for an additional 1-2 minutes until the filling thickens. Adjust with water if it appears too dry or too soupy. Remove from heat and cool the filling.

Roll out the dough and cut into circles or rectangles, as preferred.

Place a spoonful of the apple filling on half of each dough piece, leaving a border. Brush the edges lightly with water, then fold over and press the edges with a fork to seal.

Heat oil in a deep pan to about 350°F. If you don't have a thermometer, test with a small piece of dough; it should bubble and float.

Fry the pies in small batches for 2-3 minutes per side, or until golden brown.

Drain the fried pies on a cooling rack or paper towels. Dust with powdered sugar or roll in cinnamon sugar while still warm before serving.