Preheat the oven to 375°F (190°C). Grease a 9×13-inch baking dish.
In a large skillet, heat olive oil over medium heat. Sauté the garlic and mushrooms until the mushrooms are golden brown and tender, about 5-7 minutes. Add the spinach and cook until wilted (or heated through if using frozen spinach). Season with salt and pepper. Set aside.
To make the béchamel sauce, melt butter in a medium saucepan over medium heat. Whisk in the flour and cook for 1-2 minutes, until lightly golden. Gradually add the milk, whisking constantly until smooth. Bring the mixture to a simmer and cook for 5-7 minutes until thickened. Season with salt, pepper, and a pinch of nutmeg (if using).
In the prepared baking dish, spread a thin layer of béchamel sauce. Lay down a layer of lasagna noodles over the sauce. Add a portion of the spinach and mushroom mixture, followed by dollops of ricotta and a sprinkle of mozzarella and Parmesan. Repeat the layers, ending with a final layer of noodles and béchamel sauce. Top with the remaining mozzarella and Parmesan.
Cover the dish with aluminum foil and bake for 25 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the top is golden and bubbly.
Let the lasagna rest for 10 minutes before slicing and serving. Garnish with fresh parsley, if desired.