Preheat the oven to 350 degrees F. Grease a 2-quart baking dish and set aside.
Cut or tear the bread into 1-inch cubes and spread it evenly on 2 baking sheets. Toast the bread in the oven until completely dry and beginning to crisp and brown, about 20 minutes. Transfer to a large mixing bowl.
Melt 2 tablespoons of the butter in a large skillet over medium-high heat. Add the mushrooms and a few pinches of salt and saute, stirring occasionally, until golden brown, about 6 to 8 minutes. Add celery, onion, 2 tablespoons butter, and thyme. Once the butter has melted, cook, stirring frequently, until the vegetables have softened, about 5 minutes. Add sage and remaining 4 tablespoons butter. Add chicken broth to skillet and stir to combine. Season with salt and pepper, to taste.
Transfer toasted bread cubes to a large bowl. Pour the chicken broth mixture over the bread cubes and toss to combine until the bread cubes absorb the liquid. Pour the mixture into the greased baking dish, and sprinkle with parsley. Bake in the center of the oven until heated through and the top is golden brown, about 40 minutes. Remove the stuffing from the oven and allow to cool about 15 minutes before serving.