Place the brisket in a large pan with the pickling seasoning and enough water to fill the pan halfway. Cover and cook for 3 hours. Let cool partially, and then refrigerate to cool completely (for at least 3 hours total if you cut the brisket into pieces, or overnight if cooling it whole).
Dice the brisket and puree in a food processor until a paste forms (some chunks are fine). Add the sauerkraut, cream cheese and Swiss cheese and mix well. Shape the mixture into little spheres the size of golf balls; set aside.
In a large heavy-bottomed saucepan fitted with a deep-frying thermometer, pour enough vegetable oil to fill the pan about a third of the way. Heat over medium heat until the oil reaches 350 degrees F.
In three separate containers put the flour, buttermilk, and breadcrumbs mixed with parsley. Take a sphere and coat in the flour, dredge in the buttermilk and then coat in the breadcrumbs. Repeat with the remaining spheres. Fry in batches--making sure all the fritters are submerged--until golden brown, 3 to 5 minutes.
Serve the fritters with the Whole-Grain Honey Mustard Horseradish Dipping Sauce on the side.