In a food processor, combine flour, salt, and sugar, pulsing until mixed. Add shortening and butter, pulsing until the mixture resembles coarse crumbs. Gradually add cold ice water, pulsing just until a dough forms. Turn the dough out onto a lightly floured surface, shape it into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes to firm up.

After chilling, divide the dough in half. Roll one half on a floured surface into a 1/8-inch thick circle, ensuring it's large enough to fit in your pie dish. Carefully transfer this base to the dish, pressing it gently into the corners. Roll the second half into another circle, then cut this dough into 1/8-inch wide strips for the braid.

To form the fishtail braid, pinch together the ends of five dough strips. Split these strips, positioning two on one side and three on the other. Keep braiding by alternately taking the outer strips and moving them to the center, continuing until all strips are intertwined and the braid is complete.

Fill the prepared bottom crust with your choice of pie filling, spreading it evenly. Carefully fold the edges of the crust over the filling, creating a slight border. Brush the edges with a beaten egg to enhance browning and add richness to the crust before placing your braid around the edge, securing it with a gentle press.

Preheat your oven to 375°F. Place the pie on the middle rack and bake for 45 minutes. Watch for a golden-brown crust and bubbling filling. After 45 minutes, move the pie to the bottom rack for another 10-15 minutes to ensure even baking.