Start by hard-boiling the eggs: place them in a pot of cold water, bring to a boil, then remove from heat and let sit covered for 10-12 minutes. While the eggs cook, dice the celery stalks into 1/4-inch pieces, dice the onion into small pieces, and chop the fresh dill. Once the eggs are cooled, peel and chop them into 1/2-inch pieces. Having everything prepped before the potatoes finish cooking ensures smooth assembly.
Cut the potatoes into 1-inch cubes and place them in a large pot with cold salted water (using the 1 tbsp salt). Bring to a boil and cook for 13-15 minutes until just tender when pierced with a forkādon't overcook or they'll become mushy and fall apart when mixed. Drain thoroughly in a colander and let cool for 5 minutes so they're warm but not piping hot, which helps them absorb the dressing better.
In a large mixing bowl, combine the mayonnaise, relish, mustard, apple cider vinegar, celery seed, and paprika. Whisk together until smooth and fully combined. Season with black pepper to taste. I like to add a small pinch of extra salt here to ensure the dressing is well-seasoned, since it will be coating all the other ingredients.
Add the warm cooked potatoes directly to the bowl with the dressing and stir gently but thoroughly until all the potato pieces are evenly coated. The warm potatoes will absorb more of the dressing flavors, which is why I prefer to dress them while they're still warm rather than waiting until they cool completely.
Gently fold in the chopped eggs, diced celery, diced onion, and chopped dill from Step 1 until evenly distributed throughout the salad. Use a gentle hand to avoid breaking up the potatoes and eggs. The salad is now ready to serve at room temperature or chilled.
Transfer the potato salad to a serving dish and garnish the top with a sprinkle of extra dill and paprika for color and a hint of extra seasoning. Serve immediately at room temperature, or refrigerate until ready to serve.