Nest potatoes directly in hot coals in a charcoal grill. Surround potatoes with coals for even roasting. Roast until charred, 6 to 7 minutes. Turn potatoes and continue to roast until deeply charred outside and tender inside, 6 to 7 minutes more.

Remove potatoes to a bowl, cover with foil, and let cool to room temperature, about 30 minutes. Refrigerate until chilled, at least 1 hour, or preferably overnight.

Combine Dijon mustard, cider vinegar, rice wine vinegar, vegetable oil, kosher salt, black pepper, and cayenne pepper in a bowl for the dressing and whisk thoroughly.

Scrape, peel, or cut off any fully charred surface of potato, leaving some dark brown bits for a deeper flavor. Cut potatoes into 1/4-inch to 1/2-inch size pieces.

Add potatoes to dressing, along with red onion, celery, dill pickles, and red peppers. Toss well with a spatula until evenly mixed. Cover and refrigerate for at least 3 hours before serving, or up to overnight.