Preheat oven to 400 degrees with oven rack in middle position. Place bread on a rimmed baking sheet and bake, tossing occasionally, until crisp, about 10 minutes. Transfer to a large bowl along with walnuts and dried cranberries; set aside.
In a large nonstick skillet, heat oil over medium. Add onion, celery, and shiitakes and cook, stirring occasionally, until vegetables have softened, about 5 minutes. Add apple and continue to cook until almost tender, about 5 minutes. Add parsley, sage, and thyme and cook, stirring, until fragrant, about 30 seconds. Remove from heat; season with salt and pepper.
Add onion mixture to bowl with bread mixture; stir to combine. Add enough of the broth to thoroughly moisten the bread mixture without soaking it (there shouldn't be any excess broth in the bottom of the bowl). Spoon stuffing into a 2-quart casserole dish, cover with foil, and bake 20 minutes. Uncover, mist the top of the stuffing with olive-oil spray, if desired, and bake until golden brown, about 15 minutes more
To cook in turkey: Moisten the bread mixture with only 1 1/2 cups of the chicken broth and spoon half of the mixture into the turkey; cook turkey as preferred. For the rest of the bread mixture, add more of the broth to moisten, being careful not to soak (see above). Transfer the remaining stuffing to a 1-quart baking dish or 8-by-8-inch baking pan. Cover with foil and proceed as above.