In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add 8 ounces of sliced mushrooms and sauté for about 5 minutes until they turn golden brown. Incorporate 2 minced garlic cloves and 4 cups of fresh spinach, cooking until the spinach wilts, about 3 minutes. Season the mixture with salt and pepper to taste, then remove from heat and set aside.

In a medium saucepan, melt 4 tablespoons of butter over medium heat. Whisk in 4 tablespoons of all-purpose flour, stirring continuously for 1-2 minutes until it forms a light roux. Gradually pour in 3 cups of warm milk, whisking until the sauce thickens, about 5-7 minutes. Season with a pinch of ground nutmeg, salt, and pepper, then remove from heat.

If using traditional lasagna noodles, cook them in a large pot of salted boiling water according to package instructions until al dente, usually about 8-10 minutes. Drain and separate the noodles to prevent sticking. If opting for no-boil noodles, you can use them directly in the lasagna assembly.

Preheat your oven to 375°F (190°C). In a 9x13-inch baking dish, spread a thin layer of béchamel sauce on the bottom. Begin layering with lasagna noodles, followed by your vegetable filling, dollops of ricotta cheese, and a sprinkle of mozzarella. Repeat these layers until all ingredients are used, finishing with a layer of béchamel sauce topped with remaining mozzarella and grated Parmesan cheese.

Cover the assembled lasagna with aluminum foil and place it in the preheated oven. Bake for 25 minutes to warm through. Then, carefully remove the foil and bake for an additional 15 minutes until the cheese is bubbling and golden brown on top.

Once baked, remove the creamy spinach mushroom lasagna from the oven and let it rest for about 10 minutes. Serve warm.