Mix the flour, salt, butter, and shortening on low speed in a mixer fitted with the paddle attachment, until crumbly. With the machine running, add 2 tablespoons cold water and the egg. Beat just until the dough comes together in large clumps.
Divide the dough in half and press each portion into a 1-inch-thick round disk. Wrap each portion tightly in plastic and refrigerate until firm, at least 1 hour. (You can refrigerate the tart dough for up to 3 days; let stand at room temperature for 15 minutes before rolling. Alternatively, the dough can be frozen for up to 1 month; thaw in the refrigerator overnight before rolling.)
On a lightly floured surface with a lightly floured rolling pin, roll 1 piece of dough into a 10-inch round. Carefully transfer the dough to an 8-inch round fluted tart pan with a removable bottom, pressing the dough gently against the bottom and up the sides. Trim the edges against the side if necessary.
Line the dough with foil, then fill with dried beans or pie weights. Freeze overnight or until very hard.
To blind bake the tart shell, preheat the oven to 375°F (190°C).
Bake the frozen crust until the edges are set, about 20 minutes. Remove the foil and beans. Poke holes evenly over the bottom of the crust with a fork, then return to the oven. Bake until the bottom is set and the crust is blonde, about 8 minutes. Let cool in the pan on a rack.