1.
Preheat the oven to 356 F.
2.
Using a mandoline, slice the zucchini lengthwise into very thin slices. Sprinkle salt lightly over the zucchini on both sides and set aside to drain in a strainer. Allow to sit in the strainer for about 2 hours, then rinse the salt off completely and pat dry with a paper towel.
3.
Grease a baking pan with extra virgin olive oil and lay out a layer of zucchini slices.
4.
Add a layer of Emmental and mozzarella, a drizzle of olive oil, salt (just a pinch since the cheese will already be salty) and pepper. Repeat up to three times to form three layers of zucchini and cheese. Finish with a final layer of zucchini and grated Parmesan (if some of the other cheeses are left over, you can add them too)
5.
Bake for 30 minutes at 356 F and finish under the broiler, if need be, so that the Parmesan is browned.