Heat olive oil in a large skillet over medium heat. Add chopped onions and sauté until translucent, about 5 minutes. Stir in minced garlic and cook for an additional minute.

Add sliced mushrooms to the skillet and cook for 8-10 minutes until they release moisture and turn golden brown.

Season mushrooms with thyme, oregano, salt, and pepper. Optionally pour in white wine to deglaze the pan and let it simmer for 2-3 minutes.

Stir in halved grape tomatoes and cook for 2-3 minutes until softened. Fold in fresh spinach until wilted. Set aside.

In a medium saucepan, melt butter over medium heat. Whisk in flour and cook until golden, about 2-3 minutes. Gradually add warmed milk, whisking until thickened, about 5-7 minutes. Season with nutmeg, salt, and pepper.

Preheat oven to 375°F (190°C). Cook lasagna noodles according to package instructions until al dente. Drain and lay flat.

In a baking dish, spread a layer of Bechamel sauce. Layer with 3 noodles, half of the mushroom mixture, Bechamel sauce, and a sprinkle of cheeses. Repeat, finishing with noodles and remaining Bechamel and cheeses.

Cover with foil and bake for 25 minutes. Remove foil and bake for another 20 minutes until bubbly and golden. Let rest for 10 minutes before serving.