Place diced potatoes in a large pot with cold water and add 1 tablespoon salt. Bring to a boil over medium-high heat.
Reduce heat slightly and cook potatoes until fork-tender but not mushy, about 10-12 minutes.
Drain potatoes thoroughly and spread them on a baking sheet to cool for 15-20 minutes.
While potatoes cool, prepare the dressing by whisking together mayonnaise, sour cream, Dijon mustard, and chopped dill in a large bowl.
Add the diced red onion to the dressing mixture, along with any optional ingredients like celery, capers, or lemon juice if using.
Once potatoes have cooled to room temperature, gently fold them into the dressing using a rubber spatula, taking care not to break the potato pieces.
If using hard-boiled eggs, fold them in now with gentle movements.
Season with salt and pepper to taste, starting with 1/2 teaspoon of salt and adjusting as needed.
Cover and refrigerate for at least 30 minutes (2-4 hours is ideal) to allow flavors to meld.
Before serving, taste again and adjust seasonings if needed. Garnish with additional fresh dill or chives if desired.