Cook the lasagna noodles: Bring a large pot of salted water to the boil over high heat. Add the lasagna noodles (add one width-wise and top with one in the other direction to keep them from sticking) and cook 8 minutes. Drain and place on wax paper or a Silpat sheet.
Make the cheese mixture: In a bowl mix the ricotta, half the Parmesan, half the mozzarella, the thyme, rosemary, salt and pepper. Set the remaining cheese to the side for topping.
Make the ricotta béchamel: In a medium saucepan heat the butter over moderate heat. When sizzling, whisk in the flour and cook 1 minute. Slowly whisk in the milk and cook, whisking, for about 3 minutes. Whisk in the ricotta and Parmesan and cook, whisking, until thickened, another 3 to 4 minutes. Season with salt, pepper and nutmeg. If not using right away, place the sauce in a bowl and place a sheet of wax paper over the surface of the sauce to prevent a skin from forming. Refrigerate until ready to assemble the lasagna.
Cook the spinach: In a large skillet, heat the oil over low heat. Add the garlic and cook 1 minute. Stir in the spinach and raise the heat to moderate. Cook until the spinach is softened and tender. Set aside. Cover and refrigerate if not using immediately.
Assemble the lasagna: Place 1 cup of the tomato sauce on the bottom of a 9-inch by 13-inch glass, ceramic or cast iron baking dish. Add 5 lasagna noodles on top, overlapping them slightly. Spread half the cheese mixture on top. Add half the ricotta béchamel on top. Place all the spinach on top, spreading it out to cover all the noodles. Spread on another cup of the tomato sauce. Add the remaining noodles, overlapping them. Add the remaining cheese mixture and top with the remaining ricotta béchamel. With a spoon, spread the final cup of tomato sauce. Tuck any noodles that are sticking up or out of the pan inside. Season with salt pepper and sprinkle on the remaining 1/2 cup Parmesan and mozzarella. Cover and place in the refrigerator for up to 24 hours.
To bake: Preheat the oven to 375 degrees. Place the lasagna pan on top of a baking sheet to catch any drips. Bake on the middle shelf for about 45 minutes, or until hot and bubbling. Let rest for about 15 minutes before cutting into squares.

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