Heat the oven to 375°F. Boil egg noodles in water with the tablespoon salt until 2 minutes short of the package time, then drain and cool for 5 minutes.
Mix dry spinach, ricotta, eggs, 1/4 cup Parmesan, 1/4 teaspoon salt, pepper and nutmeg. Melt butter in a saucepan and stir in flour for 1 minute.
Gradually whisk in milk and simmer for 3 minutes until lightly thickened. Stir in remaining salt and remove from heat.
Fold warm noodles through the spinach mixture. Spread 1/2 cup white sauce in a deep 9-by-13-inch baking dish, add the noodle mixture and spoon remaining sauce evenly over it.
Scatter mozzarella and remaining Parmesan on top. Cover with foil and bake for 25 minutes, then uncover for 10 to 12 minutes until browned lightly and the center reaches 165°F.
Rest for 10 minutes and cut into 8 portions.