Step 1: Place the potato cubes in a large pot and cover with cold water by about an inch. Add 1 tablespoon of salt to the water. Bring to a boil over medium-high heat, then reduce to a simmer and cook for 10-15 minutes, or until fork-tender but not mushy. Immediately drain and let sit in the colander for 5-10 minutes to dry.
Step 2: While potatoes cool, prepare the dressing. In a large mixing bowl, combine mayonnaise, Dijon mustard, yellow mustard, apple cider vinegar (or pickle juice), sugar (if using), 1/2 teaspoon salt, and 1/2 teaspoon black pepper. Whisk until smooth.
Step 3: Add the diced hard-boiled eggs, finely diced celery, and finely diced red onion to the dressing mixture. Stir gently to combine.
Step 4: Add the slightly cooled, drained potatoes to the bowl with the dressing mixture. Gently fold everything together with a rubber spatula until all potatoes are coated, being careful not to mash them.
Step 5: Taste the potato salad and adjust seasonings as needed, adding more salt, pepper, or vinegar/pickle juice to achieve your preferred balance of flavors.
Step 6: Cover the bowl tightly with plastic wrap and refrigerate for at least 2 hours, or preferably overnight, to allow the flavors to meld and deepen.
Step 7: Just before serving, stir in the fresh chopped dill or parsley. Garnish with additional fresh herbs if desired. Serve chilled.