Place the eggs in a saucepan, cover with water, season with salt and place over medium heat. Bring to boil and cook for 2 minutes. Remove from the heat, cover and allow to sit for 11 minutes. Remove from the water and cool in ice water. Remove the shells and set aside. Slice all of the eggs in half and remove 8 of the egg yolk halves. In a mixing bowl, combine the yolks, anchovies and 2 tablespoons of the butter. Mix well. Season with pepper. Stuff the eight egg white halves with the yolk mixture. Cover with plastic wrap and refrigerate while assembling the other eggs.
Remove 8 yolks from 4 eggs. In another mixing bowl, combine the yolks, 1 tablespoon of Parmesan cheese, 2 tablespoons butter, and 2 teaspoons mustard. Season with salt and pepper. Mix well. Stuff the mixture into the egg white halves. Cover with plastic wrap and refrigerate while assembling the other eggs.
Remove the remaining 8 yolks from the last 4 eggs. In a mixing bowl, combine the yolks, the ham, 1 tablespoon of the cheese, 2 teaspoons of the mustard, and sour cream. Season with salt and pepper. Fill the egg whites with the yolk mixture.
To assemble, place all of the stuffed eggs on a serving plate. Garnish with chives.