4 tablespoons cold unsalted butter, cut into pieces
In a measuring cup, lightly beat the egg. Add enough of the ice water to measure 1/2 cup.
In a large bowl, combine the flour, salt, shortening and butter. Rub or cut the fat into the flour until the mixture resembles coarse meal.
Pour the liquid into the dry ingredients and stir the mixture into the dough.
Turn the dough onto a sheet of waxed paper and knead briefly into a smooth ball. Divide the the dough in half, pat each piece into a smooth 6-inch disk, wrap separately in plastic wrap and refrigerate for 1 hour. (If the pastry is made a day ahead, let it sit at room temperature for 10 minutes or so to prevent it from cracking when you roll it out.)