Using an Benriner slicer, carefully slice the Eggplant to about ⅛-¼ inch in thickness.
Place the slices in a large dish and sprinkle carefully with Kosher salt. Just coat the surface minimally. This step reduces the bitterness of the eggplant and will make they less greasy and easier to wrap.
Leave the slices in the salt for 15-30 minutes.
Rinse the slices and then place them in a contain of water and let them soak. This is to reduce the saltiness of the slices. Cut a piece of the eggplant and tastel. If still too salty, continue to rinse and soak. This is an important step as an appetizer that is too salty will not be appreciated by your guests.
Using a grill pan brush with EVOO and fry the slices until they have good grill marks. Remove and set aside. Fry only one side.
Combine the mozzarella and Parmesan in a bowl and mix well.
Lay them out with the grill marks facing down on the flat counter. Lay out one or two overlapping pieces of Eggplant slice and coat with the Pesto (see the following recipe).
Sprinkle the cheese over the slices.
Carefully roll them up into a rollup, and pin with a toothpick.
Spray a baking dish with cooking spray and place the rolls in the dish.
Bake at 350 degrees F for about 10 minutes.
Plate, scatter some of the Julienned Basil over the top of each roll and serve.