In a large skillet, melt butter over medium-low heat. Add onion and cook until softened. Stir in ham, corned beef, and garlic. Cook mixture, stirring constantly for 1 minute. Stir in 6 tablespoons flour and cook mixture over moderate heat, stirring occasionally, for 3 minutes.

Stir in sauerkraut, parsley, and broth; cook for 3 minutes or until thickened and paste-like. Spread mixture on a platter and chill for at least 3 hours.

Heat oil in a deep fryer to 375 degrees F (190 degrees C). In a bowl, whisk together egg, milk, and 2 1/2 cups flour. Shape sauerkraut mixture by leveling teaspoons into balls, dip them into egg mixture, and roll them in bread crumbs.

Fry balls in batches for 2 to 3 minutes or until golden brown. Transfer to paper towels to drain. Serve warm.