Cut each tomato into 3 or 4 thick slices. Lay down two or three layers of paper towel on the counter, and place tomatoes on top in a single layer. Sprinkle tomato slices evenly with salt. Let sit for 30 minutes.

Preheat the oven to 400 degrees F (200 degrees C).

Transfer Fritos into the bottom of a 9x13-inch baking dish, and arrange into an even layer. (You can add a second bag of Fritos for a thicker, crunchier bottom layer.)

Toss Cheddar cheese and Monterey Jack cheese together in a bowl. Scatter 1 ½ cups of this cheese mixture evenly over Fritos in the baking dish.

Add mayonnaise and egg to the remaining cheese in the bowl and stir until evenly combined; this will be the cheese topping. Set aside until needed.

If using, scatter cooked, crumbled bacon evenly over Fritos and cheese, then scatter onions and half of basil over bacon.

Blot salted tomatoes, with paper towels, pressing to absorb as much excess moisture as possible. Layer tomatoes on top of basil, overlapping into an even layer. Season with black pepper and oregano; scatter remaining basil evenly over seasoned tomatoes.

Dollop cheese topping in six or seven piles, equally spaced, over the surface. Spread topping evenly with a spoon or spatula almost to the edges. Sprinkle Parmesan cheese over the top.

For an optional garnish, place some additional sliced tomatoes on top and press them gently into the cheese topping. Drizzle the top with olive oil.

Bake in the preheated oven until the top is nicely browned around the edges, about 45 minutes. Let cool for 10 to 15 minutes before serving.