Preheat the oven to 375 degrees. Grease baking dish with olive oil and set aside.
Slice the zucchini lengthwise into very thin slices using a knife or mandolin. Spread the slices out on a kitchen towel, sprinkle lightly with salt, and set aside to drain.
Heat olive oil in a large skillet over medium heat. Add the chicken, onion, and garlic, salt, pepper, and nutmeg, and cook until chicken is well-browned, about 6-8 minutes.
Add the tomato sauce (reserving 2 tablespoon. for later), and stir to heat through. Stir in the spinach until wilted and then remove from heat.
In a large bowl, combine the cottage cheese, egg, and remaining pepper. Add the onion-spinach mixture and stir to combine.
To assemble the lasagna, create the first layer using the remaining tomato sauce. Layer with the zucchini slices, making sure to slightly overlap each slice to create an even layer. Over the zucchini slices, pour out half the meat sauce and spread out evenly. Pour out half of the cottage cheese mixture over the meat sauce and spread evenly.
Repeat these three steps with another layer of zucchini slices, meat sauce, and then the cottage cheese mixture.
Top with a thin layer of sliced fresh mozzarella and then cover with tin foil.
Place in the oven bake for 35 minutes, then remove tin foil and bake an additional 10 minutes, or until the cheese is bubbly and the golden brown.