Cook the pasta according to package instructions, adding a generous amount of salt to the water. Drain and rinse until cool. Peel the eggs and separate yolks from whites.

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

Add the cooked pasta to the dressing and stir to coat. Mix in the red onion, green onions, and egg whites. Garnish with additional green onions and paprika if desired. Serve immediately or refrigerate until ready to serve.