In a medium sized saucepan, melt the butter. Whisk in the flour and cook for just a minute or so. Slowly add the milk and keep whisking. Add the nutmeg, parmesan, salt and pepper whisk. Cook for a few minutes, whisking, until the béchamel has thickened slightly. Set aside to cool. Stir it once in a while so no skin forms on the top.
For the vegetables:
Preheat the oven to 375 degrees F.
In a large Le Creuset, heat the olive oil, and add the onion and carrot and start to sauté. Once soft, add the remaining chopped vegetables and season with salt and pepper. Cook for 15-20 minutes until starting to caramelize and get soft. Add the marinara sauce and parmesan and stir to combine. Keep over medium low heat.
Spray a 13x9 baking pan with cooking spray. Spoon some béchamel thinly on the bottom of the pan. Start with a layer of noodles, a layer of béchamel, some vegetables, a layer of basil vinaigrette and then a layer of a cheese. Repeat layers until you have 3 layers of noodles. On top of the last layer, finish with béchamel and the remaining cheeses. Cover tightly with a greased piece of foil.
Bake for 50 minutes, remove foil, increase heat to 450 and bake for 15 minutes more until top is golden brown, cheese is bubbling and the noodles are crisp on the edges. Let sit for 15 minutes before slicing.
Notes
Leftover veggies are easy to incorporate. If you don't have quite enough, just sauté the new/fresh veggies first to release water, then add the already cooked ones to heat through before proceeding.