Preheat oven to 375F.
Place a large saucepot over medium heat and melt the butter. Sprinkle the flour over the butter and cook for about 1 minute. Whisk in the milk and chicken stock, and bring the sauce up to a bubble. Add in the nutmeg and season with salt and freshly ground black pepper. Simmer until the sauce thickens, 3-4 minutes.
Assemble the lasagna by ladling a small amount (about 1/2 cup, just eyeball it) of the sauce into the bottom of a 13x9" baking dish. Lay three of the lasagna noodles over the sauce and top them with about 1/3 of the spinach. Top with about 1 cup of the sauce and about 1 cup of the shredded cheese (about 2 generous handfuls). Make two more layers of the lasagna by laying down three lasagna noodles, about 1/3 of the spinach, 1 cup of the sauce and about 1 cup shredded cheese for each layer. Top the lasagna off with the last three noodles, the remaining sauce, and the remaining shredded cheese.
Cover the pan with aluminum foil and bake the lasagna for 30 minutes. Remove the foil from the baking dish and bake another 15 minutes until the cheese is melted and the sauce is bubbly.
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