Make the filling: Drain the ricotta in a fine sieve set over a bowl for 1 hour, or longer if the ricotta is very wet.

If using fresh spinach, stem and rinse it well; don't dry the leaves. In a 12-inch skillet over medium-high heat, cook the spinach until wilted, 3 to 5 minutes. Drain well, squeeze out the excess moisture, and chop finely. If using thawed frozen spinach, squeeze it dry.

Melt the butter in a 10- or 12-inch skillet over medium-low heat and add the onion. Cook until the onion is soft and translucent, 5 to 8 minutes. Add the garlic and cook for about 1 minute. Add the spinach and toss it for 1 or 2 minutes to coat it with the butter. Transfer the spinach mixture to a bowl and let it cool to room temperature. Add the ricotta, Parmigiano, eggs, salt, pepper, and nutmeg. Mix well. You should have about 4-1/2 cups.

Cook the noodles: Bring a large pot of salted water to a boil. Prepare a large bowl of ice water. Slip the noodles, two or three at a time, into the boiling water and cook them until they're tender and pale, 3 to 5 minutes (thinner noodles will cook more quickly). To make sure they're done, taste a small piece. If it's still tough, it needs a little more cooking (fresh pasta should not be cooked al dente like dried pasta).

Carefully scoop the noodles out of the pot with a large wire skimmer and slide them into the ice water to stop the cooking. When they're cool, layer them between clean dish towels until you're ready to assemble the lasagne (The noodles will keep this way for up to 2 hours).

Assemble the lasagne: Position a rack in the center of the oven and heat the oven to 350 degrees F. Choose a baking dish that's about 9x12 inches and 3 inches deep, or about 10x14 inches and 2 inches deep. Spread 1/2 cup of the tomato sauce in a sparse layer on the bottom of the baking dish. Cover the sauce with a slightly overlapping layer of cooked noodles, cutting them as needed to fill the gaps. With a spatula, spread one-third of the spinach and ricotta filling (about 1-1/2 cups) over the first layer of noodles. Then spread one-third of the remaining tomato sauce (about 1-1/3 cups) and one-third (1/2 cup) of the cream sauce over the filling. Sprinkle 1/3 cup of the Parmigiano on top. Add a new layer of noodles, overlapping them slightly, and repeat the layers as instructed above, using all of the filling and ending with the Parmigiano, to make a total of three layers (you may not need all the pasta). Dot the top with the butter cubes.

Put the baking dish on a baking sheet and bake until heated through and bubbling at the edges, 45 to 50 minutes. Remove from the oven and let rest for 10 to 15 minutes before serving.