Preheat oven to 425º F. Prepare pie crust for blind baking by placing unbaked pie crust into pie plate, crimping edges and pricking bottom and sides with a fork for venting. Then, line unbaked pie crust with a sheet of parchment paper and fill with dried beans. Bake pie crust until lightly golden brown, about 20 minutes. Remove from oven, remove dried beans and parchment paper (storing for later use) and set aside. Reduce oven to 350º F.
In the meantime, spread tomatoes onto a baking sheet lined with paper towels. Sprinkle tomato slices with salt and then top with another layer of paper towels. Allow tomatoes to rest for at least 15 minutes to dry as much as possible.
Layer tomatoes and onion slices in pie crust until filled. Sprinkle with black pepper and drizzle with olive oil. Sprinkle on chopped basil.
Mix together cheddar and Parmesan cheeses in a small bowl with mayonnaise. Spread on top of Tomato Pie to ensure completely covered.
Bake Tomato Pie at 350º F for approximately 40 minutes.
Remove from oven and allow to rest for about 5 minutes before slicing.