In a medium saucepan over medium heat, melt the butter until bubbly. Whisk in the flour, stirring continuously until smooth and slightly golden. Gradually add milk and let it simmer until thickened. Stir in nutmeg, salt, and pepper, then set aside.

Heat olive oil in a large skillet and sauté onion and garlic until fragrant. Add red and yellow bell peppers, then zucchini and spinach; season with salt and pepper, cooking for an additional 2 minutes. Remove from heat and let cool.

In a large mixing bowl, combine ricotta, Parmesan, and beaten egg, mixing well. Fold in the cooled vegetable mixture gently.

Bring salted water to a boil in a large pot. Cook lasagna noodles according to package instructions until al dente. Drain and rinse with cold water to prevent sticking.

Spread a thin layer of white sauce in a 9x13 inch baking dish. Layer noodles, half of the vegetable cheese mixture, and mozzarella cheese. Repeat layers and finish with remaining noodles and white sauce, topped with mozzarella.

Preheat oven to 375°F (190°C). Cover lasagna with foil and bake for 25 minutes. Uncover and bake for an additional 20-25 minutes until golden and bubbling.

Allow the lasagna to rest for 10-15 minutes before slicing to let the layers set.