In a medium saucepan, melt the butter over medium heat. Add the flour and whisk until smooth, about 2 minutes. Gradually add the warm milk, whisking constantly, until the sauce is thick, smooth, and creamy, about 10 minutes (do not allow the béchamel sauce to boil). Remove from the heat and stir in the salt, pepper, and nutmeg. (The sauce can be made up to three days ahead. Cool, then cover and refrigerate.)
Preheat oven to 400°. In a medium bowl, stir together ricotta, spinach, 1/2 cup Parmesan cheese, salt and pepper. Set aside. After noodles have been drained and béchamel sauce has been made, cover the bottom of a 13- by 9-inch baking dish with a thin coating of béchamel sauce. Add a layer of noodles. Cover with 1/3 of the ricotta mixture. Sprinkle on 1/3 of the mozzarella. Cover with some of the béchamel. Repeat layers twice saving enough béchamel to cover the top of the lasagna. On top of the last amount of mozzarella cheese, add another layer of noodles. Top with remaining béchamel and then sprinkle with some Parmesan. Cover with aluminum foil and bake for 40 minutes or until sides are bubbly. Uncover and cook for another 5-10 minutes. Allow to cool for 10-15 minutes before serving so lasagna can set up.