Divide eggplants into 1 - 1 1/2 inch slices and salt lightly.
Fry in olive oil on high just until browning on both sides.
Meanwhile, combine ricotta, two-thirds of the mozzarella, half of the parmesan, egg, basil, and a pinch of salt in a bowl and set aside.
Layer a 9 X 13 baking pan as follows: (1) thin layer of sauce ; (2) layer of fried eggplant ; (3) 2 cloves of the garlic ; (4) half of the ricotta mixture ; (5) layer of sauce ; (6) remainder of eggplant ; (7) remainder of garlic ; (8) remainder of ricotta mixture ; (9) remainder of sauce ; (10) remainder of shredded mozzarella and shredded parmesan.
Bake at 370 degrees Fahrenheit for 30-40 minutes until golden and bubbly.
Turn off the oven and leave for another 20-30 minutes before cutting.