How to Make It
In a large pot, combine the ham hocks with the onion, leek, celery, carrot, peppercorns, bay leaf, thyme and 1 teaspoon of salt. Cover with 1 inch of cold water and simmer over moderately low heat, partially covered, until the meat is tender, about 2 1/2 hours. Strain the stock into a medium bowl. Transfer the ham hocks to a work surface to cool, then remove the meat from the bones and finely shred (discard the other solids). Transfer the ham to a medium bowl, stir in the parsley and season with pepper. Moisten with about 2 tablespoons of stock, stirring until the mixture comes together. Save the remaining stock for another use.
Meanwhile, in a blender, combine the egg yolk, vinegar and mustard. With the machine running, slowly add 1/2 cup of the oil until the dressing is emulsified. Transfer to a small bowl and season with salt and pepper. Cover and keep chilled.
In a saucepan, cover the quail eggs with 1 inch of cold water. Bring to a simmer, then cook over moderate heat for 2 1/2 minutes. Immediately transfer to a bowl of ice water. Let stand for 3 minutes, then peel carefully.
Divide the meat mixture into 8 portions, about 3 tablespoons each. Place the meat in the palm of your hand, top with a quail egg, then enclose the egg in the meat. Transfer to a plate and refrigerate for 30 minutes.
In a saucepan, heat the remaining oil to 350°. Arrange the flour, breadcrumbs and beaten eggs in separate bowls; season each with salt and pepper. Dip each egg patty in the flour, then the eggs, then the breadcrumbs, shaking off any excess. Working in 2 batches, fry over moderate heat, turning once, until golden brown, 2 to 3 minutes. With a slotted spoon, transfer to paper towels to drain. Spoon some mustard dressing onto plates. Halve the eggs and place on the plates. Sprinkle with celery salt and serve with beet greens, if desired.