Bring a large pot of water to a boil over high heat, then add cubed Yukon Gold potatoes and cook until tender, about 12-15 minutes. The potatoes should offer little resistance when pierced with a fork.

Drain the potatoes and spread them on a sheet pan to cool to room temperature, about 10 minutes. You want them dry on the surface so the dressing clings instead of becoming watery.

In a bowl, whisk together mayonnaise, yellow mustard, Dijon mustard, white vinegar, sugar, salt, and pepper until smooth and creamy, about 1-2 minutes. Stop when the mixture looks uniform in color with no mustard streaks.

In a large bowl, combine cooled potatoes, diced celery, finely diced onion, and chopped hard-boiled eggs. Toss gently so the eggs stay in small pieces.

Pour the mustard dressing over the potato mixture and toss well until every piece is coated. Let it sit at room temperature for 10 minutes so the dressing starts to absorb.

Cover and refrigerate the salad for 2 hours before serving. Chill until firm and well flavored, with a thicker, clingy mustard coating.