Place the potatoes in a large saucepan and add enough water to cover. Bring to a boil. Cook, partially covered, for 25 to 30 minutes, or until fork tender.
Drain and cool.
Peel and cut the potatoes into 1-inch chunks and place in a medium bowl.
Add the eggs, salt, cayenne, black pepper, celery, green onions, and parsley.
Combine mayonnaise, mustard, and Crystal hot sauce and add to the bowl. Toss until well coated.
Serve immediately or refrigerate and serve slightly chilled.