Chop vegetables uniformly. Place the mixed vegetables on a baking sheet pan. Drizzle with olive oil, salt and pepper. Roast for 20 minutes at 425 degrees. Remove and give them a quick toss and continue roasting for 10-15 minutes more until vegetables are soft. Set aside to cool slightly. Reduce oven temperature to 350 degrees F.
Spray a 13x9 baking pan with cooking spray. Spoon some bechamel thinly on the bottom of the pan. Start with a layer of noodles, a layer of bechamel, some vegetables, and then a layer of a little parmesan and mozzarella. Repeat layers until you have 3 layers of noodles. On top of the last layer, don't use any vegetables, just some bechamel and the remaining cheeses. Cover tightly with foil.
Bake for 50 minutes, remove foil and bake for a little longer until top is slightly golden. Let sit for 15 minutes before slicing.