Place the potatoes in a large pot and cover with cold water by 1 inch. Add a generous pinch of salt. Bring to a boil, then reduce to a simmer and cook 10–12 minutes, until fork-tender but not falling apart.
Drain the potatoes and spread them out on a baking sheet to cool for about 15 minutes. (Cooling helps prevent a watery salad.)
Meanwhile, make the dressing: in a large bowl, whisk together mayonnaise, BBQ sauce, Dijon mustard, pickle relish, garlic powder, salt, pepper, and hot sauce (if using).
Add the cooled potatoes to the bowl along with chopped eggs, diced onion, celery, pickles, and parsley. Gently fold until everything is evenly coated.
Taste and adjust seasoning. Add an extra drizzle of BBQ sauce if you want a smokier, sweeter finish.
Cover and refrigerate for at least 2 hours (overnight is even better). Serve chilled.