Preheat oven to 350°. Cook chorizo in a 12-in. frying pan over medium-high heat until browned, stirring often and breaking meat into small chunks, about 8 minutes. Measure fat from pan; you should have 1/4 cup (if needed, add oil). Add celery, onion, garlic, oregano, and cayenne, if using; sauté until slightly softened, about 4 minutes. Add apples and stir to coat.
Transfer mixture to a very large bowl. Add broth to pan and stir to loosen browned bits; pour into bowl. Stir in parsley and bread. Spoon stuffing into a buttered 9- by 13-in. baking dish, mounding it.
Bake stuffing until browned and center reaches at least 160°, 50 to 60 minutes; drape with foil if it starts to get dark.
Make ahead: Up to 1 day through step 2, covered and chilled; bake about 1 hour.
Note: Nutritional analysis is per serving.