If using frozen spinach, defrost and squeeze the water out before cooking.
In a medium saucepan with extra virgin olive oil, sauté the garlic over medium heat until golden brown. Add the spinach. Toss just until wilted, about 5 minutes. Season with salt and pepper, remove from heat and set aside.
BECHAMEL SAUCE: In a small, heavy saucepan, melt the butter over low heat. Add the flour, whisking continuously until the roux is thick. Add the milk gradually, whisking continuously. Sprinkle nutmeg and salt into the mix. When the bechamel sauce becomes thick, remove it from the heat. To thin the sauce if it cools, add more milk.
In a blender or food processor, combine the pumpkin with 1/2 cup bechamel sauce. Set aside.
Prepare a pot of salted boiling water. Cook the lasagna sheets according to the package instructions, or to al dente. With a slotted spoon, remove the cooked sheets from the pot and pat them dry with a paper towel.
Preheat the oven to 375 degrees F.
Spray or rub extra-virgin olive oil in a 9x13-inch baking dish. Pour a thin layer of bechamel sauce into the dish. Layer the ingredients. Start with a lasagna sheet. Add pumpkin, spinach, Parmesan, and bechamel sauce. Repeat for 2 more layers. Place one more lasagna sheet for the final layer. Top it with the bechamel sauce and Parmesan cheese. Drizzle with some extra virgin olive oil.
Bake in the preheated oven for 30 minutes or until the top turns golden.