Make the filling: Heat a medium skillet over high heat until it begins to smoke lightly. Remove the pan from the heat, add the butter and toss in the pears and cranberries. Return to high heat and cook until the fruit is slightly tender, about 5 minutes. Add the sugar, cornstarch, corn syrup, cloves, lemon juice and orange zest. Mix to blend and cook over high heat until the syrup thickens, about 5 minutes. Remove from the heat and scoop into a bowl; refrigerate until cool. Remove and discard the cloves.
Make the crust: Butter the bottom and side of a 9-inch pie pan and refrigerate. In a large bowl, whisk the flour, sugar and salt. Work in the shortening and butter with your fingers until the mixture resembles small peas. Add up to 1/3 cup ice water, about 2 tablespoons at a time, mixing with your fingers until the dough comes together. Transfer the dough to a flat surface, roll it into a ball and cut in half. Shape each half into a smaller ball. Flatten the balls, wrap each in plastic and refrigerate at least 30 minutes.
Transfer the dough to a lightly floured surface. Using a rolling pin, roll out one half until it is at least 4 to 5 inches wider than the pie pan and 1/8 to 1/4 inch thick. Gently fit the dough into the pie pan, pressing it into the bottom and side. Trim, leaving a 1-inch overhang; put the pan in the refrigerator. Roll the second half of the dough 1/8 to 1/4 inch thick for the top of the pie. Put it on a baking sheet; refrigerate both crusts about 15 minutes.
Preheat the oven to 425 degrees F. Assemble the pie: Pour the filling into the crust. Brush the edge with the beaten egg; cover with the top crust. Pinch around the edge to seal the top and bottom crusts together, removing the excess dough with a paring knife. Use a paring knife to cut an X opening, 1 1/2 to 2 inches across, in the center of the crust; fold back the dough. Put the pie on a rimmed baking sheet.
Bake the pie, 10 minutes. Lower the temperature to 375 degrees F and continue baking until the crust is light golden brown, 30 more minutes. Let cool completely on a rack. Sprinkle with sugar.