Preheat the oven to 350 degrees F. Heat 1 stick butter in a large skillet over medium heat. Add the onion, celery, apple, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring, until tender, about 10 minutes. Stir in the parsley and sage and cook until softened, about 3 more minutes.
Put the cornbread in a large bowl and add the vegetable-apple mixture. Add the pecans and dried fruit; toss to combine. Add 4 cups chicken broth 1 cup at a time, tossing after each addition. The cornbread should feel moist but not mushy; add 1 more cup broth ¼ cup at a time if needed. Melt the remaining 1/2 stick butter and stir into the stuffing.
Butter a 3-quart baking dish. Add the stuffing mixture and lightly press down. Cover with foil and bake 40 minutes. Uncover and bake until the top is dry and browned, about 30 more minutes. Let stand 20 minutes before serving.
Make the stuffing 2 to 3 days ahead; cover and refrigerate. Reheat at 325 degrees F, covered, until hot, then drizzle with broth or melted butter if it looks dry. Bake, uncovered, a few more minutes until crisp.