Put the eggs in a medium saucepan and cover with water to about an inch above the eggs.
Cover the saucepan and place it over high heat; bring to a full rolling boil. Remove the pan from the heat and let stand, covered, for 18 minutes.
Pour off the hot water and cover the eggs with cold water. Peel the eggs under running water.
Slice the eggs in half (lengthwise). Scoop the egg yolks into a medium bowl and place the egg white halves, cut side up, on a tray or egg plate.
With a fork, combine the yolks with the ham, finely chopped green onions and dill pickle, 2 tablespoons of mayonnaise, dill pickle juice, and the mustard. Taste and add salt and pepper, as needed. If desired, add more mayonnaise. Mix well.
Using a small spoon or scoop, mound the egg yolk mixture into the egg white halves and sprinkle with paprika if desired.