Hard boil the eggs: Place eggs in a saucepan, cover with cold water, bring to a boil, then remove from heat, cover, and let sit for 12 minutes. Transfer to an ice bath, then peel.

Cook the pasta in a large pot of salted boiling water until just slightly past al dente. Drain and rinse under cold water to stop cooking. Place in a large bowl.

Slice the hard-boiled eggs in half. Remove the yolks and place them in a separate medium bowl. Chop the egg whites and add them to the bowl with the pasta.

Mash the egg yolks with a fork until very fine. Add the mayonnaise, mustard, relish, vinegar, sugar, salt, pepper, onion powder, and garlic powder. Whisk until smooth and creamy.

Pour the dressing over the pasta and egg whites. Stir gently until everything is heavily coated.

Cover the bowl tightly and refrigerate for at least 2 hours (or overnight) to let flavors meld and the pasta absorb the dressing.

Before serving, stir well. Dust generously with paprika and garnish with fresh parsley. Serve chilled.