Arrange the tomato and onion slices in a single layer on a paper towel-lined baking sheet and sprinkle with salt. Let sit for 1 to 2 hours.
Preheat the oven to 350 degrees F.
Fit the pie crust into a 9-inch pie plate and crimp the edges. Prick the bottom and sides with a fork. Line the crust with aluminum foil and fill with pie weights or dried beans. Bake until the edges of the crust are just golden, 20 to 25 minutes. Remove the foil and weights and continue to bake until the bottom of the crust is dry and brown, another 15 to 20 minutes. Cool completely.
Mix together the Cheddar, mozzarella and mayonnaise in a medium bowl. Season with 1/2 teaspoon salt and a few cracks of black pepper.
Transfer the tomatoes and onions to a dry paper towel and pat dry. Liberally season the tomatoes with cracked black pepper. Arrange a third of the tomatoes in a single layer in the pie crust, overlapping slightly. Sprinkle a third of the basil over the tomatoes and top with a third of the onions. Repeat twice with the remaining tomatoes, basil and onions. Spread the mayonnaise mixture over the top of the onions.
Bake until the topping is golden brown and bubbling, 30 to 35 minutes. Let cool completely. Garnish with basil leaves. Serve at room temperature.
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