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

In a large skillet, heat olive oil over medium heat. Sauté onion until soft, about 5 minutes. Add garlic and cook another 1 minute.

Add mushrooms and thyme. Cook, stirring occasionally, until mushrooms release moisture and become golden, about 8–10 minutes. Season with salt and pepper. Set aside.

In a separate saucepan, melt butter over medium heat. Whisk in flour and cook 1 minute. Gradually pour in warmed milk, whisking constantly until smooth and thickened, about 3–4 minutes.

Remove from heat and stir in Parmesan cheese. Taste and adjust salt and pepper as needed.

Spread a thin layer of béchamel on the bottom of a 9×13-inch baking dish.

Layer 4 noodles over the béchamel. Top with one-third of the mushroom mixture and one-third of the remaining mozzarella. Spoon over béchamel to cover lightly. Repeat for two more layers.

Finish with noodles topped by remaining béchamel and mozzarella.

Cover with foil and bake for 25 minutes. Remove foil and bake another 10–12 minutes, until cheese is bubbly and golden.

Let rest 10 minutes before slicing. Garnish with parsley if desired.