Lightly butter a 9x13-inch baking dish. Preheat oven to 350 degrees F.
In a large skillet over medium heat, cook the sausage, stirring frequently, until sausage is cooked through. Remove to paper towels to drain. Wipe out the skillet and melt the butter over medium-low heat. Add the onion and celery and cook, stirring, until the vegetables are softened, about 5 to 7 minutes.
In a large mixing bowl, toss the bread cubes with the herbs and seasonings. Add the vegetables with the butter and the drained sausage. Stir in chicken broth until well moistened, but not mushy. Pack gently into the prepared baking dish and cover tightly with foil. Bake for 25 minutes. Remove foil and broil for about 3 to 4 minutes, or just until browned on top.