To prepare the pie dough, beat together the butter, sugar, and salt for 3 minutes on medium speed in the bowl of an electric mixer. Add the egg and beat for 30 seconds. Add the flour and water and beat for 15 seconds. Turn off the machine, scrape down the sides of the bowl, and beat again for 10 seconds. Sccop up the dough with your hands and form it into a 1-inch thick disk. Wrap in plastic wrap and refrigerate for at least 1 hour.
Melt the butter over medium-high heat in a medium-sized saute pan. Saute the peaches and sugar until the sugar is dissolved, about 2 minutes. Add the jam or preserves, cayenne, and white pepper; cook, stirring frequently, for 3 minutes. Cool for 10 minutes.
On a lightly floured surface, roll out the dough into a 16 by 11-inch rectangle about 1/8 inch thick. Cut out 6 5 1/4-inch circles. (For a more free-form shape, divide the dough into six pieces and roll out.) Place the circles on a baking sheet lined with parchment or wax paper. Fill the lower half of each circle with about 1/4 cup of the cooked peaches. Fold the top half of the dough over the filling and crimp the edges securely with a fork. Refrigerate for 20 minutes before frying.
Heat 2 1/2 inches of vegetable oil to 350 degrees in a heavy 4-quart saucepan. Fry pies 2 or 3 at a time until golden brown, 1 1/2 to 2 minutes per batch. Drain on paper towels. Keep warm in a 200 degree oven until all the pies are fried. Serve immediately with ice cream.
Recipe courtesy of The Heaven on Seven Cookbook by Jimmy Bannos and John DeMers (10 Speed Press, 2001)