Cook the pasta according to package instructions, adding salt to the water. Drain and rinse until cool. 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 sieve. In a bowl, combine yolks, mayonnaise, mustard, vinegar, garlic, salt, paprika, and cayenne pepper. Whisk until smooth.

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