Preheat oven to 400°F. Place the cubed bread on a baking tray and toast in the oven until it dries out but does not get browned, about 15-20 minutes; set aside at room temperature.
In another 9x13 baking dish, toss the onions, celery, parsnip, butternut squash, apples, thyme and parsley with olive oil, salt and pepper. Bake in the pre-heated oven until the vegetables soften, about 35-40 minutes.
Remove the baking dish from the oven, add bread on top and pour the vegetable broth on over. Mix until all the broth has been absorbed. Press the mixture with the back of the spoon to level it off.
Bake uncovered until the stuffing begins to brown, about 30 minutes. Toss mixture and bake for an additional 30 minutes until some of the bread is toasted. Allow the stuffing to cool for 5-10 minutes and serve.