Place 2 eggs in a saucepan, cover with water and bring to a boil. Cook 8 to 10 minutes. Cool in a bowl of ice water. Peel the eggs, then separate the whites and chop them. Mash the yolks in a bowl, then whisk in 2 tablespoons warm water, the pickling liquid and mustard. Gradually whisk in the olive oil. Add 2 tablespoons parsley, the chives, tarragon, egg whites, pickles, 1/4 teaspoon salt, and pepper to taste.
Combine the flour, the remaining 6 tablespoons parsley and a pinch of pepper in a shallow dish. In another dish, beat the remaining egg with the milk. Dip each piece of ham in the flour to coat both sides, then dip in the milk mixture and re-dip in the flour mixture.
Heat 1/8 inch of olive oil in a large skillet over medium-high heat until sizzling. Fry the ham in batches until golden, about 4 minutes per side. Transfer to a paper-towel-lined plate. Fry the capers in the skillet until crisp, about 1 minute. Sprinkle the ham steaks with the capers, and serve the egg mixture on the side to spoon on top.