Slice the eggplant into rounds and place them on a platter in a single layer with minimal overlap.
Sprinkle with kosher salt, place another platter on top of the eggplant slices, then add something with a bit of weight (like a cast iron pan) on top. Let the slices sit for 30 minutes to an hour.
Meanwhile, cook the ground turkey in a skillet over medium heat. Once browned, remove the turkey to a plate lined with paper towels and wipe out the skillet.
Return the turkey to the skillet over medium heat, then add the tomato sauce and oregano leaves. Once the sauce is heated through, turn off the heat.
Remove the weighted item and platter from the eggplant slices, then drain off the liquid that has accumulated in the bottom platter. Rinse the eggplant and pat dry.
Heat the oil in a large skillet. One hot, add as many eggplant slices as you can fit in one layer and cook for 2-3 minutes per side until golden. Transfer the eggplant slices to paper towels to drain.
Repeat until all the eggplant slices are cooked.
Preheat the oven to 375°F. Place a few tablespoons of the tomato and ground turkey sauce in the bottom of a 13 x 9-inch baking dish.
Layer in half of the eggplant and half of the zucchini, then spread about half of the remaining tomato and ground turkey sauce on the vegetables.
Tear the basil leaves and sprinkle half of them on top of the sauce, then cover with half of the mozzarella and half of the Parmesan.
Repeat the layers.
Place in the oven and bake for 25-30 minutes until the cheese has melted.