Place diced potatoes into a large saucepan, fill 2/3 with water, a pinch of salt, and bring to a boil. Once water is boiling, continue to boil for 2-3 additional minutes. Add in cauliflower and boil for another 4-5 minutes until a fork is just able to pierce through. Do not overcook, or the cauliflower will be mushy, and no one wants that!
Once the vegetables are done cooking, drain and rinse with cold water (or place in an ice bath).
Meanwhile, mix together mayonnaise, mustard, apple cider vinegar, shallot, red pepper flakes, salt, pepper, and parsley. Add celery and red bell pepper. Mix in potatoes and cauliflower; stir until all is coated. Garnish with chives and/or parsley.