Unfold the pie crust according to package directions. Line a 9-inch tart pan with pastry (its easier to remove the baked tart if pan has a removable bottom). Press the pastry into the fluted sides of the tart pan and trim the edges. Don't prick, but add some pie weights. Partially bake in a 450°F oven to 5 to 7 minutes or until pastry is slightly dry.
Remove from oven. Remove pie weights. Sprinkle with 1/2 cup of the mozzarella cheese. Cool in pan on a wire rack. Reduce oven temp to 375°F.
Meanwhile, cut the tomatoes into slices; drain the slices on paper towels. Arrange the tomato slices over the melted cheese in the baked crust.
In a food process bowl, combine basil and garlic; cover and process with on-off turns until coarsely chopped. Or snip the basil and mince the garlic.
In a medium mixing bowl, combine the basil-garlic mixture, the remaining shredded mozzarella cheese, the mayonnaise, the grated parmesan cheese, and pepper. Spread the mixture evenly over the tomato slices.
Bake in a 375°F oven for about 25 minutes or until cheese is golden on top. Let stand 5 minutes before cutting into wedges. Serve warm. If you like, garnish with additional basil leaves.