Fill a large pot with water and add the potato chunks. Bring the water to a boil. Cook the potatoes until they are fork-tender but still firm. This usually takes about 12 to 15 minutes.

Place the eggs in a saucepan and cover them with water. Bring the water to a boil. Turn off the heat and let the eggs sit for about 12 minutes. Cool and peel them.

Drain the cooked potatoes in a colander. Let them cool for about 15 minutes. Warm potatoes can make the dressing too thin. Cooling helps keep the salad creamy and thick.

In a small bowl, mix mayonnaise, mustard, pickle juice, salt, pepper, and paprika. Stir until smooth and creamy. This dressing gives the salad its classic flavor and rich texture.

Dice the celery, red onion, and pickles into small pieces. Small pieces spread flavor evenly throughout the salad. Chop the boiled eggs into bite-sized pieces as well.

Place the cooled potatoes in a large bowl. Add the eggs, celery, onion, and pickles. Pour the dressing over everything. Gently mix until all ingredients are coated evenly.

Sprinkle chopped parsley over the salad. Fold it in carefully. The parsley adds freshness and color. It also gives the salad a bright homemade appearance.

Cover the bowl and refrigerate for at least one hour. Chilling allows the flavors to blend beautifully. The salad tastes even better after resting in the refrigerator.