Preheat oven to 375°F (190°C). In a large bowl, mix ricotta, spinach, egg, ½ cup Parmesan, 1 cup mozzarella, salt, and a pinch of nutmeg until well combined.

Melt butter in a saucepan over medium heat. Add garlic and cook 30 seconds, stir in flour, and whisk for 1 minute. Slowly pour in warm milk while whisking constantly, simmer until thickened, about 5 minutes. Remove from heat, stir in remaining Parmesan, black pepper, and nutmeg. Adjust salt as needed.

Spread a thin layer of white sauce in a 9×13 pan. Lay 3 noodles, spread half the ricotta mixture, top with one third of the remaining sauce and some mozzarella. Repeat with 3 more noodles, remaining ricotta, another third of sauce, and more mozzarella. Finish with the last 3 noodles, remaining sauce, and all remaining mozzarella.

Cover tightly with foil, tenting slightly, and bake 25 minutes. Uncover and bake another 15 to 20 minutes until bubbly and golden. Broil the last minute if you want more color.

Let the lasagna rest for 10 minutes before slicing. Cut into squares and serve warm.