To make the pastry, mix together the flour, granulated sugar and salt. Cut in 1 cup of the shortening until the mixture resembles coarse crumbs. Add 1 of the eggs and the buttermilk and stir until it just comes together. Add a little more buttermilk if needed. Form it into a ball and refrigerate for at least an hour.
To make the pies, roll the pastry out into a large square. Trim the edges to make a rectangle. Cut into 8 to 10 long rectangles, using a butter knife.
Spoon a tablespoon or so of filling into the top half of one of the rectangles.
Use the remaining beaten eggs to seal the edges by folding the bottom half of the rectangle over the top. Then crimp the edges shut with a fork. Repeat with the other pies, filling half with apple pie filling and half with cherry pie filling.
Heat shortening in a medium, deep saucepan over medium-high heat to 350 degrees F. Fry the pies until golden brown, 2 to 3 minutes per side. Remove and immediately drain on paper towels.