Cook the pasta according to the package directions, adding a generous tablespoon of kosher salt to the water. Drain in a colander and rinse until cool. Peel the hard-boiled eggs and separate the yolks from the whites.

Chop the egg whites and set aside. In a large mixing bowl, crush the egg yolks into a fine powder or press them through a fine mesh strainer. Add the mayonnaise, Dijon mustard, white vinegar, minced garlic, kosher salt, smoked paprika, and cayenne pepper to the bowl with the egg yolks. Whisk until well combined.

Add the cooled pasta to the dressing in the bowl and stir to coat. Add the chopped red onion, green onions, and chopped egg whites. Stir to combine. Garnish with additional green onions and smoked paprika if desired. Serve immediately or cover and refrigerate until ready to serve.