Place pie crust into a 9-inch pie dish and refrigerate while preparing the tomato pie.
Slice tomatoes about 1/4-inch thick. Lay tomatoes on a baking sheet lined with paper towels. Sprinkle slices with 1 teaspoon salt, in order to remove some of the liquid. Set aside while assembling the other ingredients.
In a medium mixing bowl, combine feta cheese, mozzarella, mayo, egg, onion, basil, thyme, and pepper. Layer in pie dish, 1/3 cheese mixture, 1/3 tomatoes, and repeat laying two additional times. Tomatoes should be on top. Sprinkle parmesan cheese over tomatoes.
Bake 25 minutes, then loosely cover with foil. Continue cooking 20 minutes, or until golden, and set.