Cook the pasta according to the package directions, adding a generous pinch of salt to the water. Drain and rinse with cold water. Peel the eggs and separate the yolks from the whites.

Chop the egg whites and set aside. Mash the yolks into a fine powder or press through a fine strainer into a large bowl. Add mayonnaise, mustard, vinegar, garlic, salt, paprika, and cayenne. Whisk until smooth.

Add cooled pasta to the dressing, stirring to coat. Mix in red onion, green onions, and egg whites. Garnish with extra green onions and paprika if desired. Serve immediately or refrigerate.