In a medium saucepan over medium heat, melt butter until bubbling. Add garlic and sauté for about 1 minute until fragrant. Whisk in flour, cooking for another minute. Gradually pour in half-and-half and whole milk, whisking constantly. Allow the mixture to thicken for about 5-7 minutes, then stir in Parmesan, salt, pepper, and nutmeg.

In a large skillet, heat olive oil over medium heat. Add sliced mushrooms, sautéing until tender and browned, about 5-6 minutes. Stir in spinach, cooking until just wilted, about 2-3 minutes. Remove from heat.

In a mixing bowl, combine ricotta cheese with eggs, grated Parmesan, salt, and pepper. Gently fold in the sautéed mushroom and spinach mixture.

Preheat your oven to 375°F (190°C). In a greased baking dish, spread a thin layer of béchamel sauce on the bottom. Place a layer of lasagna noodles, followed by half of the cheese filling and a portion of mozzarella. Repeat layers, finishing with noodles, béchamel sauce, and additional mozzarella.

Cover the baking dish with aluminum foil and bake for 50 minutes. Remove the foil and bake for an additional 10 minutes or until the top is golden brown.

Once baked, let cool for about 15 minutes before slicing.