Preheat oven to 350. Cut vegetables down to about 1-2 inch pieces of equal size. Separate the harder vegetables (turnips, beets, sweet potatoes, squash) from the softer ones (potatoes, carrots). Coat harder vegetables and garlic cloves in a little olive oil and bake in a casserole dish covered with tin foil or a lid for about 20 minutes. Remove from oven and uncover. Add potatoes and other vegetables, along with an even sprinkle of salt, pepper, rosemary and another drizzle of olive oil, and bake again for about 30 minutes.
Meanwhile, brown sausages on all sides in a pan or grill. Blot excess grease with paper towels and slice into 1-inch pieces. Remove casserole from oven and arrange sausages and grape tomatoes, if using, in the dish and return to the oven for another 10-15 minutes. Toss vegetables with parsley and serve.