In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add sliced mushrooms and sauté for 5-7 minutes until they are golden and softened. Stir in fresh spinach, cooking for another 2-3 minutes until wilted. Remove from heat and set aside, allowing the savory mixture to cool slightly before assembly.

In a saucepan over medium heat, melt 4 tablespoons of butter. Whisk in ¼ cup of all-purpose flour, cooking for about 1-2 minutes until lightly golden. Gradually pour in 3 cups of whole milk while whisking continuously for 5-7 minutes, until the sauce thickens and is smooth. Season with salt, pepper, and a pinch of nutmeg.

Preheat your oven to 375°F (190°C). In a 9x13 inch baking dish, spread a thin layer of béchamel sauce on the bottom. Layer with no-boil lasagna noodles, followed by half of the sautéed mushroom and spinach mixture. Repeat the layers with more béchamel and sprinkle a generous amount of mozzarella cheese. Finish with noodles, béchamel, and top with remaining mozzarella and parmesan.

Cover with aluminum foil and bake for 30 minutes. After this time, remove the foil and bake for an additional 15-20 minutes until the top is bubbly and golden brown.

Once baked, remove from the oven and allow to rest for 10-15 minutes before slicing. Serve warm.