Heat a gas grill to medium-high or the coals in a charcoal grill to medium-hot.
Make a foil packet with potatoes and onion, drizzling with oil and seasoning with 1/2 tsp of the salt and 1/4 tsp of the black pepper before sealing. Grill, covered, 15 minutes. Turn packet over and grill an additional 15 minutes. Turn again and grill 15 minutes more or until potatoes are tender. Allow to cool.
In a large bowl, whisk mayonnaise, vinegar, mustard, sugar, garlic powder and remaining 1/2 tsp salt and 1/4 tsp pepper. Add potatoes, onions and celery. Toss to coat; stir in parsley and blue cheese.
Cover with plastic wrap and refrigerate 2 hours.