01 - Set oven to 425°F and line a large baking tray with parchment paper.
02 - Toss eggplant, zucchini, bell peppers, and mushrooms with olive oil, oregano, thyme, salt, and pepper. Spread on tray and roast for 25 minutes, stirring halfway, until tender and golden. Set aside.
03 - Lower oven temperature to 350°F.
04 - Melt butter over medium heat in a saucepan. Whisk in flour and cook for 2 minutes. Gradually add warm milk, whisking constantly until smooth. Simmer for 5-7 minutes until thickened. Season with nutmeg, salt, and white pepper.
05 - Spread a thin layer of béchamel in a 9x13 inch baking dish.
06 - Layer 3 noodles over béchamel, then half the roasted vegetables, a handful of spinach, dollops of ricotta, one-third of mozzarella and parmesan, and a generous layer of béchamel.
07 - Repeat layering with next 3 noodles, remaining vegetables, spinach, ricotta, one-third cheeses, and béchamel.
08 - Top with last 3 noodles, remaining béchamel, mozzarella, and parmesan cheeses.
09 - Cover dish with foil and bake for 25 minutes in preheated oven.
10 - Remove foil and bake an additional 15–20 minutes until golden and bubbling. Let rest for 10 minutes before serving.