1. In a 12-in. frying pan over high heat, cook mushrooms, butter, onions, celery, and garlic, stirring often, until vegetables are lightly browned, about 15 minutes. Pour into a large bowl. Add a bit of broth to pan and stir to scrape up browned bits. Add to bowl.
2. Pour 2 cups broth into bowl and add bread, artichoke hearts, poultry seasoning, and rosemary; mix well. Add salt and pepper to taste.
3. Preheat oven to 325° to 350°.
Spoon stuffing into a shallow 3-qt. (9- by 13-in.) casserole. For moist stuffing, cover with foil; for crusty stuffing, do not cover. Bake until hot (at least 150° in center) or lightly browned, about 50 minutes.
Make ahead: Up to 1 day ahead, make stuffing, put in casserole, cover, and chill. Allow about 1 hour to bake.