Preheat the oven to 400 degrees F. Lay the diced cubes of squash and parsnips out on baking sheet and toss with 3 tablespoons olive oil, salt and pepper. Roast at 400 degrees until the vegetables start to brown, 15 to 20 minutes.
In a large saute pan, melt 2 tablespoons butter with 2 tablespoons olive oil and saute the onions and celery until translucent and lightly browned. Add the cranberries and season with the sage, salt and pepper. Reduce the oven temperature to 350 degrees F.
In a large bowl, toss the cornbread cubes with the roasted squash and parsnips and the sauteed onions and celery. Drizzle the chicken stock over the stuffing and lightly toss, adding more chicken stock as needed until the bread is moist. Transfer to a 9 by 13-inch baking dish, dot with the remaining 4 tablespoons butter and bake until lightly browned and hot, about 30 minutes.