For the basil oil, in a blender, combine garlic, basil, blended oil and 2 teaspoons salt (or to taste). Blend until smooth and reserve for assembly. 

Partially peel each eggplant so that there are alternating strips of skin and flesh, then cut into ¼-inch slices on the bias. Place the slices in a mixing bowl, season with salt and allow to sit for 10 to 15 minutes. Strain to remove excess liquid.

Fry the eggplant in the frying oil in a deep fryer or Dutch oven at 325°F until golden brown, about 7 minutes, flipping halfway through. (Work in batches, as needed.) Transfer to a sheet tray or plate lined with paper towels to absorb any excess oil. Allow the eggplant to cool. 

Preheat the oven to 450°F. 

Spread ¼ cup of the tomato sauce and a few tablespoons of the basil oil on the bottom of an 8 x 8-inch oven-safe dish. Place a layer of eggplant (about 8 or 9 slices) on top of the sauce. Drizzle with 3 tablespoons of the basil oil and top with a scant cup of the sauce. Sprinkle with ½ cup of the caciocavallo and ½ cup of the Locatelli.  

Continue the process until the eggplant is finished (you should end up with about 3 layers, finishing with the cheeses on top). Bake for 15 minutes, or until the cheese is golden brown. Remove, garnish with the parsley and serve!