Mix mozzarella, Parmesan, garlic powder, 1/4 tsp. pepper and a pinch of nutmeg. In a separate bowl, whisk ricotta with egg and spinach until blended and smooth. Season with salt and pepper.
Spread 1/3 of sauce over bottom of a large, heavy skillet. Arrange 2 pasta sheets on top. Spread half of spinach mixture over pasta, then scatter 1/3 of mozzarella mixture on top. Top with 2 more pasta sheets, then spread with 1/3 of sauce. Sprinkle with 1/3 of mozzarella mixture. Place another 2 sheets on top and pour over remaining sauce. Break remaining sheets of pasta into large pieces and use them to fill in around edges of skillet.
Dollop remaining spinach mixture over top, and sprinkle on remaining mozzarella mixture. Transfer skillet to stovetop and cook, covered, over medium-low heat until top is firm, 20 minutes. Remove from heat and set aside, covered, for 5 to 10 minutes before serving.