Bring a pot of water to a boil over high heat and boil the cubed red potatoes until tender, about 8–12 minutes, until a fork slides in easily. Keep the boil steady so the cubes cook evenly.

Drain the potatoes and let them cool to room temperature for 10–15 minutes, until no steam is rising from the surface.

Add the cooled potatoes to a mixing bowl and combine with the chopped dill pickles, diced celery, and finely diced red onion.

Whisk the mayonnaise, dill pickle juice, Dijon mustard, salt, and black pepper in a separate bowl until the dressing looks smooth and evenly colored.

Pour the dressing over the potato mixture and toss well until every piece is coated, with no dry spots visible.

Fold in the chopped fresh dill, then stir gently just until distributed and bright green flecks are visible throughout.

Cover and refrigerate for 2 hours, until the salad is chilled through and the flavors taste well blended.