Make pastry: Blend together flour, butter, shortening, Parmesan, pepper, and salt in a bowl with your fingertips or a pastry blender (or pulse in a food processor) until mixture resembles coarse meal with some roughly pea-size lumps. Drizzle 2 tablespoons ice water over and gently stir with a fork (or pulse in food processor) until incorporated.
Gently squeeze a small handful: If it doesn't hold together without falling apart, add more water, 1 tablespoon at a time, stirring (or pulsing) after each addition until incorporated, continuing to test. Do not overwork dough, or it will become tough.
Turn out dough onto a work surface and divide into 2 portions. With heel of your hand, smear each portion once in a forward motion to help distribute fat. Gather both portions of dough into 1 ball, then pat into a disk. Chill, wrapped in plastic wrap, until firm, about 1 hour.
Preheat oven to 375 degrees F.
Roll out dough on a lightly floured surface into a 12-inch round and fit into a 9-inch round tart pan with a removable rim. Fold excess dough in to make sides. Lightly prick tart shell all over with a fork.
Line the shell with foil and fill with pie weights, or rice. Bake in middle of oven 20 minutes. Carefully remove foil and weights and bake until golden, about 15 minutes more. Cool in pan on a rack.
Fill tart shell: Remove side of pan and slide shell onto a platter. Arrange 1/3 of mozzarella in bottom of shell and drizzle with 1/3 of pesto. Arrange 1/3 of tomato slices, overlapping, on top of cheese. Season with salt and pepper. Repeat layering twice.
Cook's note: Tart shell can be made 1 day ahead and kept, covered, at room temperature.
Recipe courtesy of Gourmet Magazine