Make the Pie Crust: Add the flour, salt and sugar to the work bowl of a food processor and pulse a few times to combine. Scatter the butter pieces over flour mixture, tossing to coat butter with some flour. Cut the butter into the flour with five 1-second pulses. Add the shortening and continue pulsing (about four more 1-second pulses) until the flour is pale yellow and resembles coarse cornmeal with butter bits no larger than small peas. Turn the mixture into medium bowl.
Sprinkle 4 tablespoons of ice water over the flour mixture. Use a rubber spatula to mix; press down on the dough with the broad side of the spatula until the dough sticks together, adding up to 1 tablespoon more ice water if the dough will not come together. Shape the dough into two balls with your hands, one slightly larger than the other. Flatten into 4-inch-wide disks. Dust lightly with flour, wrap in plastic, and refrigerate for 30 minutes before rolling out.
Preheat oven to 350 degrees F.
Prepare the Filling: While the dough is chilling, prepare the pie filling. Brown the sausage over medium heat in a large sauté pan, breaking it up into bite-size pieces as it cooks. Cook until the sausage is no longer pink in the middle, adding the onions during the last few minutes of cooking.
Using a slotted spoon, transfer the sausage and onions to a large mixing bowl. Add all the remaining ingredients and mix well until thoroughly combined.
On a lightly floured surface, roll out the smaller piece of pie dough into a circle about ⅛-inch thick. Transfer the dough to a 10-inch regular pie plate or a 9-inch deep dish pie plate.
Transfer the filling to the dough-lined pie plate. There is a lot of filling, so you'll want to pack it tightly into the pie dish, mounding it slightly in the center. Roll out the other dough round and place over the filling. Trim top and bottom edges to ½ inch beyond pan lip. Tuck this rim of dough underneath itself so that folded edge is flush with pan lip. Flute edging or press with fork tines to seal. Cut four slits at right angles on dough top. With a fork, beat together the egg yolk and heavy cream, and brush over the top and crust of the pie.
Bake the pie until the crust is golden brown and the cheese is bubbling through the slits on top, about 50 minutes. Let the pie sit for at least 30 minutes before serving. Any leftovers should be refrigerated.
Notes
If you cannot find basket cheese, you can substitute any other mild, semi-soft cheese in its place.