Preheat the oven to 375 degrees F. Melt 1 stick butter in a large skillet over medium heat. Add 2 cups each diced onions and celery, 2 chopped apples and 1 tablespoon each minced sage and thyme; season with salt and pepper and cook 5 minutes. Add 3 cups chicken broth and bring to a simmer. Whisk 2 eggs with 1/4 cup chopped parsley in a large bowl; add 16 cups cubed stale country white bread, then pour in the vegetable-broth mixture and toss. Transfer to a buttered 3-quart baking dish and dot with more butter. Cover and bake 30 minutes, then uncover and bake until golden, 20 more minutes.