Heat oven to 325 degrees. Bake ciabatta bread cubes until lightly toasted, about 15 minutes. Set aside. Increase oven temperature to 375 degrees.
In skillet over medium-high heat, melt 1 tablespoon butter. Cook sausage, breaking meat into medium pieces, until browned, about 8-10 minutes. Transfer sausage to large bowl; set aside.
Add remaining butter to skillet; cook carrots, onions and celery until soft, for 5-7 minutes, and transfer to bowl with sausage.
In large bowl, mix bread cubes, chicken broth, olive oil, parsley, rosemary and salt and pepper, to taste. Add vegetable and sausage mixture to bread cubes mixture and combine.
Spread evenly in greased 9-by-13-inch baking dish. Bake until golden brown and bread is slightly crisp on top, 30-35 minutes. Garnish with additional parsley before serving.
Tip: Recipe can be made one day before and refrigerated overnight.