Add flour, sugar, shredded cheddar cheese, and salt to the bowl of a food processor. Pulse a few times to combine. Cut the cold butter into cubes. Add to the flour mixture along with the vegetable shortening. Turn processor on and let run for 5 seconds. Then, drizzle in cold water. Keep processing until mixture begins to clump.
Pour dough mixture onto a clean surface. Using your hands, pull the dough together into one ball. Cut ball in half and form two discs of the same size and shape. Cover each disk in plastic wrap. Refrigerate until cold, at least 2 hours.
Remove one disk of dough from the refrigerator and let it sit on the counter for 10 minutes to soften up. Preheat oven to 400 degrees.
Once dough is ready, roll it out into a disk using a rolling pin. The dough should be 10½ to 11 inches in diameter. Gently fold rolled dough in half and place onto 9 inch pie pan that is 2 inches deep (deep dish pie pan). Unfold the dough so that it is covering the dish completely. Let the dough lay into the dish so that it is not stretched or pulled. Fold over excess edges and press into a smooth or fluted edge, ensuring that the whole outside edge is the same thickness. Chill while you make the filling.