**If roasting fresh vegetables rather than using leftover cooked vegetables, preheat oven to 375 degrees.
Place carrots, butternut squash, and onions on a roasting pan and drizzle with olive oil and sprinkle with salt and pepper. Roast 30 minutes or until just becoming tender when poked with a fork, but still firm in the middle. Add the green beans to the pan and toss to coat with the oil. Return to the oven and roast until beans are tender crisp, about 5 minutes longer. Stir in the peas and set aside.
Heat the butter in a large pot over medium low heat. Whisk in the flour and cook for one minute, whisking constantly. Whisk in the milk until smooth. Whisk in the vegetable broth, parsley, and thyme. Simmer until thickened, about 3 minutes. Stir the vegetables (and any turkey, chicken, etc. if using) into the sauce. Taste and add more salt and pepper if necessary.
Transfer the vegetable mixture to oven safe bowls or a baking dish. Lay phyllo dough on the counter and quickly spray cooking spray or brush butter between layers. Cut layered dough into squares that will just fit over the bowls or baking dish. Place on top and cut a small slit so that steam can escape.
Bake uncovered until dough is golden brown, about 20 minutes.