In a saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes until smooth. Gradually whisk in the milk until smooth. Bring to a simmer, stirring constantly. Reduce heat and simmer for about 5-7 minutes, or until thickened. Stir in the nutmeg, salt, and pepper. Remove from heat and set aside.

Heat the olive oil in a large skillet over medium heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook for 1 minute more. Add the bell peppers and zucchini and cook until tender-crisp, about 5-7 minutes. Stir in the spinach, salt, and pepper. Remove from heat and let cool slightly.

In a large bowl, mix the ricotta cheese, Parmesan cheese, and egg. Stir in the cooled vegetable mixture.

Cook the lasagna noodles according to package directions. Drain and rinse with cold water.

Preheat the oven to 375°F (190°C). Spread a thin layer of white sauce in the bottom of a 9×13 inch baking dish. Layer 3 lasagna noodles over the sauce. Spread half of the vegetable filling over the noodles. Sprinkle with 1 cup of mozzarella cheese. Repeat the layers: white sauce, noodles, vegetable filling, and another cup of mozzarella cheese. Top with the remaining noodles and white sauce. Sprinkle with the last cup of mozzarella cheese.

Cover the baking dish with foil and bake for 25 minutes. Remove the foil and bake for an additional 20-25 minutes, or until the cheese is melted and bubbly and the lasagna is heated through.

Let the lasagna stand for 10-15 minutes before serving.