Slice the eggplants into ⅜" (1cm) slices. Try your best to get the slices as even as possible.
Purging using the microwave method (see notes below for oven method)Season all the eggplant slices with salt but be careful not to overseason them.
Line a plate with a clean kitchen towel. Add the salted eggplant slices in an even layer on the towel. Fold the towel over so that the slices are sandwiched in between towels.
Cover with another plate and repeat the process until you can get all of your eggplant slices covered with towel. Finish the last layer with a heavy plate.
Microwave the plates for 3-5 minutes on high or until eggplant slices begin to soften slightly. You may need to work in batches.*Be careful as the plates will be super hot.*
Remove the slices from plates and gently press out any moisture using paper or more kitchen towels. Set aside on another plate or tray.
Slice and drain the mozzarella on paper towel.
Rough chop the basil and set aside.
Set oven temperature to 375°F/190°C.
Once thickened, use a hand blender to quickly pulse the tomatoes into a sauce. Alternatively, you can use a food mill to also remove the seeds.
Get a large non-stick pan on medium-high heat and have another tray with paper towel ready. Fry the eggplant slices in half vegetable oil and half olive oil until golden brown. Drop the slices in the pan away from you. *Make sure the slices are dried well otherwise the oil may splatter.*
Drain the seared eggplant slices on paper towel.
Add a little tomato sauce to the bottom of the casserole dish.
Layer the fried eggplants in an even layer, allowing them to overlap slightly. Then add the ⅓ of both kinds of cheeses, basil and a little freshly cracked black pepper.Repeat 1 more time.
Finish the top of the Melanzane with some tomato sauce and cheese but no basil.
Bake at 375°F/190°C for 25-35 minutes or until the top is golden brown.
Let the eggplant parm sit for 10 minutes at room temperature to allow it to soak up any excess moisture.Serve with fresh basil leaves and more fresh Parmigiano cheese on top.