Preheat the oven to 450 degrees F (230 degrees C). Press pie pastry into a 9-inch pie pan; prick the bottom and sides with a fork.
Bake in the preheated oven until lightly browned, 10 to 12 minutes. Remove from the oven and cool completely; reduce the oven temperature to 350 degrees F (175 degrees C).
While the crust is cooling, place tomato slices in a single layer in a colander; sprinkle with salt. Let sit for about 10 minutes to release moisture. Blot excess moisture with a paper towel.
Arrange 1/2 of the tomatoes in a layer over the bottom of the cooled crust, overlapping the slices. Sprinkle with 1/2 each of the garlic, basil, Cheddar, and mozzarella. Repeat layers once more, then spread mayonnaise over the top.
Bake in the preheated oven until cheese is melted and bubbling, about 30 minutes. Cool on a wire rack.
