Bring a large pot of salted water to a boil and add the eggs. Once the water returns to a boil, remove from heat, cover the pot, and let the eggs sit for 20 minutes—this gentle method gives you perfectly cooked eggs with creamy yolks and no gray ring. While the eggs are cooking, bring a separate pot of salted water to a boil, add the cubed potatoes, and simmer for 15 minutes until just tender but not falling apart. Once done, drain the potatoes and spread them on a sheet pan to cool faster.

While the potatoes and eggs cool, finely dice the celery and red onion—keeping them uniform in size ensures even distribution throughout the salad. Once the eggs have cooled enough to handle, peel them under cool running water and chop them into bite-sized pieces. I like to peel the eggs while they're still slightly warm, as the shell comes off much more easily.

In a large mixing bowl, combine the mayonnaise, mustard, and relish, whisking them together until smooth and well blended. This creates your flavor base and ensures the seasonings are evenly distributed before you add the vegetables. Add the salt and black pepper to taste—I like to season conservatively at first and adjust after everything is combined, since the potatoes will absorb some of the flavor as it sits.

Add the cooled potatoes from Step 1, chopped eggs from Step 2, diced celery, and diced red onion to the dressing. Using a rubber spatula, gently fold everything together until the potatoes and eggs are evenly coated, being careful not to break them apart. Taste and adjust seasoning if needed. Refrigerate for at least 30 minutes before serving to let the flavors meld.