Cut eggplants lengthwise into 1/4 inch slices.
Arrange one layer in the bottom of a large colander. Sprinkle evenly with salt. Repeat with remaining eggplant slices, salting, until all eggplant is in the colander.
Weigh down the slices with a couple of plates and let drain for 2 hours. The purpose of this step is to have the eggplant release some of its moisture before cooking.
Add tomatoes, garlic and 1/3 cup olive oil to a food processor. Process until combined.
Season with salt and pepper, to taste. Set aside.
When eggplant has drained, press down on it to remove excess water.
Remove from colander and wipe off the excess salt.
Lay slices out on paper towels to remove all the moisture.
Pour flour into wide, shallow bowl. Set aside.
Pour breadcrumbs into another wide, shallow bowl. Set aside.
Pour beaten eggs into a third wide shallow bowl. Set aside.
Pour in about 1/2 inch of olive oil into a large, deep skillet. Place over medium heat.
When oil is hot and shimmering, dredge eggplant slices first in the flour, turning to coat both sides.
Then dip in the beaten egg, again covering completely.
Finally place in the bread crumbs, press to coat completely.
Working in batches, slide coated eggplant into hot oil. Fry until golden brown on both sides, turning once, about 3 minutes per batch.
Using tongs, remove to a paper towel-covered plate to drain.
Preheat oven to 350°F.
Lightly brush a 15 x 10 x 2-inch glass baking dish with olive oil.
In the bottom of the baking dish, spread 1 cup of tomato sauce.
Arrange 1/2 of the eggplant over the sauce.
Cover the eggplant with another 1/3 of the sauce.
Scatter 1/2 of the Parmesan and 1/2 of the mozzarella over the sauced eggplant.
Repeat with the remaining eggplant, sauce, Parmesan and mozzarella.
Place in preheated oven. Bake until hot and just beginning to brown, about 30 minutes.
Serve immediately.