To make the stuffing: Place the bread cubes on a baking sheet, and let them sit uncovered, overnight, to become a bit stale. This will help give the stuffing better texture., Preheat the oven to 350°F. If you'll be baking the stuffing outside the bird, lightly grease a 2-quart casserole dish or similar-size pan., Melt the butter in a large frying pan, and sauté onions and celery slowly until soft, about 20 minutes. Remove them from the heat., Place the bread cubes in a large bowl. Spoon the onion-celery mixture over the bread., Add the parsley, poultry seasoning, salt, and pepper, and toss the mixture until it's thoroughly combined. A large spoon or spatula works well for this task., Whisk together the broth and eggs, and stir into the bread mixture., Spoon the stuffing into the turkey. Or spoon it into the prepared pan, and cover the pan loosely with aluminum foil., If you're baking it in a pan, bake the stuffing for 1 hour, until it's firm and no liquid is evident. For a crusty top, remove the foil about 20 minutes before the end of the baking time., To make the gravy: Combine the cornstarch with 1/2 cup of the broth, whisking it or shaking it in a jar until no lumps remain., Place the cornstarch/broth and the remaining broth into a saucepan. For extra flavor and richness, stir in pan drippings or melted butter; omit this step, if desired., Cook the gravy over medium heat, stirring frequently, until it thickens. Season to taste with salt and pepper.