In a medium saucepan over medium heat, melt butter. Whisk in all-purpose flour and cook for 1-2 minutes until golden and bubbly. Gradually add milk while stirring continuously for about 5-7 minutes until thickened. Stir in nutmeg, salt, and black pepper, then set aside to cool.

In a large skillet, heat olive oil over medium heat. Add chopped onion and sauté until softened, about 5 minutes. Stir in minced garlic, diced bell peppers, and sliced zucchini. Cook until tender, approximately 5-7 minutes, then incorporate thawed and squeezed spinach, adding salt and pepper to taste. Allow this mixture to cool slightly.

In a large mixing bowl, combine ricotta cheese, grated Parmesan cheese, and beaten egg. Mix thoroughly with a fork until well combined. Gently fold in the cooled vegetable filling until fully incorporated.

Bring a large pot of salted water to a boil and cook lasagna noodles according to package instructions until al dente. Drain and rinse under cold water to stop cooking. Lay flat on a clean kitchen towel.

Preheat your oven to 375°F (190°C). Spread a layer of the prepared white sauce in a 9x13 inch baking dish. Layer with three lasagna noodles, half of the vegetable filling, and a sprinkle of shredded mozzarella. Repeat, finishing with noodles, white sauce, and mozzarella on top.

Cover with foil and bake for 25 minutes. Remove foil and bake for an additional 20-25 minutes or until cheese is golden and bubbly.

Let the lasagna rest for 10-15 minutes before slicing.