Cook pasta by boiling salted water in a large pot, then add pasta and cook as directed until al dente. Drain and cool under cold water.

Prepare eggs by peeling them, separating the yolks and whites. Chop the whites into small pieces.

Make dressing by mashing yolks and mixing with mayonnaise, mustard, vinegar or lemon juice, garlic, salt, paprika, and cayenne until smooth.

Combine cooked pasta with dressing, fold in chopped egg whites, red onions, and green onions, mixing well.

Serve immediately or chill for 30 minutes, garnishing with additional green onions and smoked paprika.