Preparation Chop liver and transfer to small bowl; cover and refrigerate. Bring broth, neck, heart, and gizzard to boil in heavy large saucepan. Reduce heat to medium; simmer 1 hour. Strain broth into medium bowl; reserve. Remove meat from neck; place in small bowl. Chop heart and gizzard; add to bowl with neck meat. Heat 2 tablespoons oil in medium skillet over medium heat. Add onion and garlic; sauté until tender, about 3 minutes. Add reserved liver; sauté until cooked through, about 4 minutes. Add chopped neck meat, heart, and gizzard, 1 1/2 cups of reserved broth, and 1/4 cup oil. (Dressing can be made 2 days ahead; cover and refrigerate dressing and any remaining broth separately.) Preheat oven to 400°F. Divide bread cubes between 2 rimmed baking sheets. Drizzle 2 tablespoons oil over bread on each sheet; toss to coat. Toast bread in oven until golden brown, turning once, about 10 minutes. Transfer to large bowl. Add mushrooms, celery, celery root, 1 tablespoon parsley, and oregano to bread. Bring dressing to simmer; remove from heat. Stir in vinegar. Pour dressing over bread mixture; toss. If desired, drizzle remaining broth by tablespoonfuls over bread mixture to moisten. Sprinkle remaining chopped parsley over. Let stand at least 10 minutes and up to 1 hour.
Preparation Chop liver and transfer to small bowl; cover and refrigerate. Bring broth, neck, heart, and gizzard to boil in heavy large saucepan. Reduce heat to medium; simmer 1 hour. Strain broth into medium bowl; reserve. Remove meat from neck; place in small bowl. Chop heart and gizzard; add to bowl with neck meat. Heat 2 tablespoons oil in medium skillet over medium heat. Add onion and garlic; sauté until tender, about 3 minutes. Add reserved liver; sauté until cooked through, about 4 minutes. Add chopped neck meat, heart, and gizzard, 1 1/2 cups of reserved broth, and 1/4 cup oil. (Dressing can be made 2 days ahead; cover and refrigerate dressing and any remaining broth separately.) Preheat oven to 400°F. Divide bread cubes between 2 rimmed baking sheets. Drizzle 2 tablespoons oil over bread on each sheet; toss to coat. Toast bread in oven until golden brown, turning once, about 10 minutes. Transfer to large bowl. Add mushrooms, celery, celery root, 1 tablespoon parsley, and oregano to bread. Bring dressing to simmer; remove from heat. Stir in vinegar. Pour dressing over bread mixture; toss. If desired, drizzle remaining broth by tablespoonfuls over bread mixture to moisten. Sprinkle remaining chopped parsley over. Let stand at least 10 minutes and up to 1 hour.