Preheat oven to 375 degrees. Spray a deep pie pan with cooking spray or brush with olive oil. Set aside.
Slice the tomatoes into approximately 1/4 to 1/3-inch slices. Discard the tops of the tomatoes.
Line a rimmed baking sheet with two layers of paper towels or a thick, clean kitchen towel. Generously salt both sides of the tomatoes then place on the prepared baking sheet to drain for approximately 30 minutes. (This can also be done on any flat surface.)
Place dry paper towels or a clean, dry kitchen towel over the tomatoes and blot dry with gentle pressure to get as much moisture out as possible.
Combine 1 cup of the mozzarella, 1 cup of the white cheddar, mayonnaise, eggs, garlic and black pepper to preference in a small bowl.
Spread approximately 1/3 cup of the cheese combination on the bottom of the prepared baking dish.
Layer 1/3 of the tomatoes over the cheese combination, slightly overlapping the tomatoes.
Spread half of the remaining cheese combination over the first layer of tomatoes. Sprinkle with half of the scallions and tear the leaves from one sprig of the basil into pieces and distribute evenly.
Place a second layer of tomatoes over the cheese/scallions/basil followed by the remaining cheese/scallions/basil.
Top with the remaining tomatoes and sprinkle with the remaining cheese.
Bake for 35-40 minutes or until the cheese is lightly browned, bubbling and the center is at least 165 degrees when a thermometer is inserted. Let stand 10-15 minutes before cutting into wedges.