Prepare the ricotta filling: If using fresh spinach, set a large skillet over high heat. (If using thawed frozen spinach, skip to Step 2.) When hot, add oil and half the fresh spinach. Season and sauté until wilted, about 3 minutes. Transfer to a baking sheet to cool. Repeat with remaining spinach.

While spinach cools, combine ricotta, mozzarella, Parmesan, basil, and salt in a large bowl.

Squeeze out any water from cooled spinach, chop finely, and add to cheese mixture. Mix thoroughly, then taste and adjust seasoning. Cover and set aside until ready to assemble lasagna.

Prepare the béchamel: In a large pot over medium heat, melt butter. Whisk in flour, reduce heat, and cook for about 15 minutes, stirring regularly. Slowly whisk in milk, increasing heat to medium while whisking until thickened, about 2 minutes. Add salt, pepper, and nutmeg to taste.

Continue cooking béchamel until thick and smooth, about 10 to 15 minutes. Adjust seasoning if needed. Strain if lumpy and cover to prevent a skin.

Preheat oven to 400°F (200°C).

Bring tomato sauce, béchamel, and ricotta filling to room temperature if cold.

Boil water in a large pot. Prepare a colander in a baking dish nearby.

Season the water generously with salt. Lay pasta sheets in the boiling water for 2 minutes until light in color and flexible. Remove and rinse under cold water, then proceed with assembly.

Spoon béchamel into a baking pan and coat the bottom.

Cover the bottom with pasta sheets, allowing ends to hang over the edges.

Crumble ricotta mixture over pasta as the first layer, then add more pasta sheets.

Spread tomato sauce evenly over the next layer and cover with pasta.

Spread béchamel and sprinkle Parmesan over the next pasta layer.

Alternate remaining layers using ricotta, tomato sauce, béchamel, and pasta until used up.

Fold overhanging pasta over the last layer, cover with remaining béchamel, and wrap tightly in foil.

Bake for 40 minutes, then uncover and add mozzarella for another 20 minutes until golden brown.

Cool for at least 15 minutes before slicing. Leftovers can be refrigerated or frozen.