Preparation Preheat oven to 350°F. Bake bread cubes on large rimmed baking sheet until dry and beginning to brown, about 12 minutes. Place bread in large bowl and cool. Melt 4 tablespoons butter in heavy large skillet over high heat. Add onions and celery; sauté until tender and beginning to brown, about 10 minutes. Add apples; sauté until tender and beginning to brown, about 10 minutes. Add mixture to bread. Melt 1 tablespoon butter in same skillet. Add ham; sauté 5 minutes. Add ham to bread; mix in herbs and nutmeg. Add broth to same skillet and bring to boil, scraping up any browned bits. Pour broth into small bowl; cool. (Stuffing and broth can be prepared 1 day ahead. Cover separately; chill.) Preheat oven to 350°F. Butter 13x9x2-inch glass baking dish. Beat eggs into broth; mix into stuffing. Transfer stuffing to prepared dish. Bake uncovered until cooked through and browned on top, about 35 minutes.
Preparation Preheat oven to 350°F. Bake bread cubes on large rimmed baking sheet until dry and beginning to brown, about 12 minutes. Place bread in large bowl and cool. Melt 4 tablespoons butter in heavy large skillet over high heat. Add onions and celery; sauté until tender and beginning to brown, about 10 minutes. Add apples; sauté until tender and beginning to brown, about 10 minutes. Add mixture to bread. Melt 1 tablespoon butter in same skillet. Add ham; sauté 5 minutes. Add ham to bread; mix in herbs and nutmeg. Add broth to same skillet and bring to boil, scraping up any browned bits. Pour broth into small bowl; cool. (Stuffing and broth can be prepared 1 day ahead. Cover separately; chill.) Preheat oven to 350°F. Butter 13x9x2-inch glass baking dish. Beat eggs into broth; mix into stuffing. Transfer stuffing to prepared dish. Bake uncovered until cooked through and browned on top, about 35 minutes.