Cook potatoes in boiling water until potatoes are tender. Combine potatoes and butter in a large mixing bowl; and beat at medium speed with an electric mixture until all is smooth.

In another bowl, add egg yolks, parsley, salt, pepper and nutmeg, and mix well.
Divide potato mixture into 10 portions. Wrap each portion around a cheese slice.
Lightly dust each with flour dip into the egg mixture, and then coat with bread crumbs. Chill these patties for about 20 minutes in the refrigerator.

Pour the oil to the depth of 4 inches and heat to 340 degrees F. Fry a few at a time, 8 minutes turning once. Serve immediately.