Prep the potatoes: Rinse the cut potatoes to remove excess starch. Place them in a large pot and cover with cold water by about an inch.
Add 1 tablespoon kosher salt.
Cook until tender: Bring to a gentle boil, then lower to a simmer. Cook 10–14 minutes, until the potatoes are just tender when pierced with a fork. Don’t overcook.
Drain and steam-dry: Drain the potatoes well.
Return them to the warm pot and let them sit uncovered for 5 minutes so steam evaporates. This keeps the salad from getting watery.
Season while warm: Sprinkle 1–2 tablespoons dill pickle brine over the warm potatoes and gently toss. This adds flavor from the inside out.
Make the dressing: In a large bowl, whisk together mayonnaise, Dijon, sour cream or yogurt, vinegar, garlic powder, paprika, salt, and pepper until smooth.
Add the mix-ins: Stir in the chopped dill pickles, celery, red onion, and fresh dill.
Fold in the chopped hard-boiled eggs, if using.
Combine: Add the warm potatoes to the bowl and gently fold everything together until coated. Taste and adjust salt, pepper, and pickle brine as needed.
Chill: Cover and refrigerate at least 1 hour (4 hours is even better). The flavor develops as it chills.
Serve: Give it a light stir before serving.
Top with a sprinkle of dill, paprika, and black pepper for color.