In a large bowl, combine flour, Parmesan cheese, pepper and salt; cut in the butter and shortening until crumbly. Gradually add water, tossing with a fork until dough forms a ball. Cover and refrigerate for 1 hour or until easy to handle.
On a lightly floured surface, roll out pastry to fit a 9-in. fluted tart pan with removable bottom. Transfer pastry to tart pan; trim pastry even with edge. Line unpricked pastry shell with a double thickness of heavy-duty foil. Bake at 375° for 20 minutes. Remove foil; bake 15 minutes longer. Cool on a wire rack.
Remove sides of tart pan. Place crust on a serving plate. Arrange mozzarella over crust with slices overlapping. Spread with pesto. Arrange tomato slices in an overlapping pattern on top. Season with salt and pepper.