Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish and set aside.

Make white sauce by melting butter in large saucepan over medium heat. Whisk in flour and cook 2 minutes stirring constantly.

Gradually add warm milk while whisking continuously. Cook, stirring frequently, until sauce thickens, about 8-10 minutes.

Remove from heat and stir in Parmesan cheese, salt, white pepper, and nutmeg. Set aside to cool slightly.

Heat olive oil in large skillet over medium-high heat. Sauté zucchini strips until lightly golden, 3-4 minutes per side. Season and set aside.

Cook mushrooms in same skillet until golden and moisture evaporated, about 6-8 minutes. Season and set aside.

Wilt spinach in skillet with splash of water, then drain thoroughly and squeeze out excess moisture.

Combine ricotta cheese, eggs, fresh basil, oregano, and 1 cup mozzarella in large bowl. Mix until well combined.

Spread thin layer of white sauce on bottom of prepared baking dish.

Layer 4 noodles, half ricotta mixture, half vegetables, and one-third remaining white sauce.

Repeat with 4 noodles, remaining ricotta, remaining vegetables, and another third white sauce.

Top with final 4 noodles, remaining white sauce, remaining mozzarella, and grated Parmesan.

Cover with foil and bake 45 minutes. Remove foil and bake additional 15-20 minutes until golden and bubbly.

Let rest 15 minutes before slicing to allow layers to set properly.