In a 2-quart pot, melt 5 tablespoons of butter over medium heat. When butter has completely melted, add the flour and whisk until smooth, about 2 minutes. Gradually add the milk, whisking constantly to prevent any lumps from forming. Continue to simmer and whisk over medium heat until the sauce is thick, smooth and creamy, about 10 minutes. The sauce should be thick enough to coat the back of wooden spoon. Remove from heat and add the nutmeg and tomato sauce. Stir until well combined and check for seasoning. Set aside and allow to cool completely.
In a saute pan, heat extra-virgin olive oil. When almost smoking, add the ground beef and season with salt and pepper. Brown meat, breaking any large lumps, until it is no longer pink. Remove from heat and drain any excess fat. Set aside and allow to cool completely.
In a medium sized bowl, thoroughly mix the ricotta and eggs. Season with salt and pepper. Set aside.
Into the bottom of a 13 by 9-inch baking dish, spread 1/3 of the bechamel sauce. Arrange the pasta sheets side by side, covering the bottom of the baking dish. Evenly spread a layer of all the ricotta mixture and then a layer of all the spinach. Arrange another layer of pasta sheets and spread all the ground beef on top. Sprinkle 1/2 the mozzarella cheese on top of the beef. Spread another 1/3 of the bechamel sauce. Arrange the final layer of pasta sheets and top with remaining bechamel, mozzarella and Parmesan cheeses. Cut the remaining 2 tablespoons of butter into 1/4-inch cubes and top lasagna.
Line a large baking sheet with aluminum foil. Place lasagna dish on top, cover and put on the middle rack of the oven and bake until top is bubbling, about 30 minutes. Remove cover and continue to bake for about 15 minutes.
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