Whisk the white sauce: Melt butter in a saucepan, whisk in flour and cook 1 minute. Slowly whisk in milk, garlic, nutmeg, salt, and pepper. Simmer 5 to 7 minutes until thickened, then set aside.

Sauté the vegetables: Heat olive oil in a skillet over medium-high heat. Cook onion, zucchini, bell pepper, and mushrooms until softened, about 8 minutes. Add spinach and stir until wilted, about 2 minutes. Season and drain any liquid.

Mix the ricotta filling: Stir together ricotta, egg, Parmesan, salt, and pepper until smooth.

Layer the lasagna: Spread a thin layer of white sauce in a 9×13-inch dish. Layer noodles, half the vegetables, half the ricotta mixture, a third of the mozzarella, and a third of the sauce. Repeat. Top with final noodles, remaining sauce, and remaining mozzarella.

Slice and serve: Cover with foil and bake at 375°F for 30 minutes. Uncover and bake 15 to 20 minutes more until golden and bubbly. Rest 10 minutes, then slice and serve.