Place eggs in large pot and cover with 3 inches of water. Bring to a boil, remove from heat, cover and let rest for 10 minutes. Transfer eggs to a bowl of ice water and begin peeling the shells from the eggs. Slice the eggs lengthwise in half and remove yolks.
In a bowl, mash the yolks with the mayonnaise, diced scallions, dry mustard, salt and pepper. Using a spoon, scoop the filling into the egg white halves, carefully arrange on a platter, and sprinkle with paprika and fresh chopped parsley.