Cut the potatoes into quarters and put them in a big pot. Add cold water until it covers them by an inch. Bring to a boil, then add 1 tablespoon salt. Boil for 13–15 minutes until fork-tender.
Step 2: Make the dressing
While the potatoes cook, mix the mayonnaise, relish (including juice), mustard, vinegar, celery seeds, paprika, 1 teaspoon salt, and some pepper in a bowl. Stir it smooth.
Step 3: Prepare the mix-ins
Chop your hard-boiled eggs, celery, sweet onion, and dill. Set them aside.
Step 4: Combine everything
Drain the soft potatoes and peel off loose skins. Chop into 1/2-inch chunks. Put them in a large bowl while still warm. Mix in the dressing gently until well-coated. Then fold in the eggs, celery, onion, and dill. Taste and adjust salt and pepper if needed.
Step 5: Chill and serve
Cover the bowl and refrigerate for at least 4 hours. For best flavor, I always make this potato and egg salad recipe a day ahead. It really lets everything soak in.
Notes
If you can’t find Yukon Gold potatoes, Russet potatoes work great too. This mustard potato salad recipe gets better after resting, so plan to chill it overnight if you can.