Lay tomato slices in a single layer on paper towels to drain for at least 30 minutes.
Preheat oven to 425 degrees. Place pie crust into pie plate. Trim edges. Sprinkle cornmeal evenly over crust.
In a small bowl, combine mayonnaise, vinegar, sugar, salt & pepper. In a separate bowl, mix two cheeses together.
To assemble pie, sprinkle 1/2 cup of cheese to bottom of pie. Layer 1/3 of tomato slices in single layer. Spread with half of the mayonnaise mixture and sprinkle with 1/2 of the scallions and basil and about 3/4 cup of cheese. Layer 1/3 of tomato slices topped with remaining mayonnaise, scallions, basil and 3/4 cup of cheese. Top with remaining tomato slices and remaining cheese.
Bake for 35-40 minutes. Cover edges of crust with foil if becoming too brown. Allow pie to cool for at least an hour before serving.