Preheat oven to 450 degrees F. On a large greased baking sheet arrange acorn squash wedges, cut sides down. Roast about 20 minutes or until tender, turning once halfway through roasting time.
In a large skillet cook parsnips, onion, and garlic in hot oil over medium heat for 3 minutes, stirring occasionally. Stir in butternut squash, chicken broth, snipped or dried thyme, salt, and pepper. Bring to boiling. Reduce heat; simmer, covered, over medium-low heat about 15 minutes or until vegetables are tender. Stir in cranberries. Cook 1 to 2 minutes more or until most of the liquid has evaporated.
Serve parsnip mixture over acorn squash wedges. Garnish with fresh thyme sprigs.