Place the potato chunks in a large pot and cover with cold water. Add 1 teaspoon salt and bring to a boil over high heat. Reduce heat to medium and simmer for 10-12 minutes, until potatoes are fork-tender but not falling apart.
Drain the potatoes in a colander and spread them out on a baking sheet to cool completely. This helps prevent them from becoming mushy when mixed.
In a small bowl, whisk together mayonnaise, Dijon mustard, apple cider vinegar, fresh dill, and black pepper until smooth. Set the dressing aside.
Once the potatoes are cool, transfer them to a large mixing bowl. Add the chopped celery, red onion, and sliced radishes.
Pour the dressing over the potato and vegetable mixture. Gently fold everything together with a spatula until evenly coated, being careful not to crush the potatoes.
If using, fold in optional add-ins like chopped hard-boiled eggs or crumbled bacon at this stage.
Cover the bowl with plastic wrap and refrigerate for at least 1 hour to allow the flavors to meld. Serve chilled or at room temperature.