Place lasagna noodles and enough water to cover in a 2-quart microwave-safe, ovenproof casserole dish. Cover and microwave on high until noodles are softened, about 4 minutes. Drain off water and arrange noodles on a plate to cool. Dry casserole dish.
Meanwhile, heat oil in a large non-stick skillet. Add garlic and sauté until fragrant, 30 seconds. Add spinach and 1 tablespoon water, then stir to coat leaves and cover pan. Cook, shaking pan occasionally, until wilted, about 1 minute. Spread cooked spinach out on a cutting board to cool, then finely chop.
In a medium bowl, combine 1 cup of the mozzarella, ricotta, ¼ cup of the Parmesan cheese, egg, nutmeg, pepper & cooled chopped spinach. Place a few tablespoons of spinach mixture along the lasagna & spread to almost the end of the noodle and roll up. Place rolls seam-side down in casserole; pour remaining sauce (gravy) over rolls. Sprinkle with remaining mozzarella and Parmesan. Cover with foil and bake 25 minutes. Uncover, and bake until cheese bubbles, 5 to 10 minutes more. Let stand 5 minutes before serving.