01 - Preheat the oven to 425°F. Line a large baking sheet with parchment paper for easy cleanup.
02 - Arrange zucchini, eggplant, bell peppers, and onion on the prepared baking sheet. Drizzle with olive oil, then sprinkle with oregano, salt, and black pepper. Toss vegetables thoroughly to coat evenly.
03 - Roast vegetables for 20 to 25 minutes, stirring halfway through cooking time, until tender and lightly browned. Remove from oven and set aside. Reduce oven temperature to 375°F.
04 - In a medium saucepan over medium heat, melt butter. Add flour and whisk constantly for 1 to 2 minutes until mixture bubbles but does not brown.
05 - Gradually whisk in warm milk while stirring constantly until smooth. Continue cooking for 5 to 7 minutes until sauce thickens noticeably. Stir in salt, nutmeg, white pepper, and Parmesan cheese. Remove from heat.
06 - Spread a thin layer of white sauce across the bottom of a 9x13-inch baking dish. Arrange 3 lasagna noodles over the sauce. Top with one-third of roasted vegetables, one-quarter of white sauce, and one-third of mozzarella cheese.
07 - Repeat the layering process two more times with noodles, vegetables, sauce, and mozzarella. Finish with remaining white sauce, mozzarella, and sprinkle 1/3 cup Parmesan cheese over the top.
08 - Cover baking dish tightly with foil. Bake at 375°F for 30 minutes until heated through.
09 - Remove foil and continue baking for 15 to 20 minutes until cheese turns golden brown and sauce bubbles around edges. Let rest for 10 minutes before slicing to set. Garnish with fresh basil if desired.