Peel and cube potatoes. Boil in salted water till tender. Drain and mash with 1/2 tsp salt (more or less), butter, milk, and pepper. Cool slightly and add egg yolk. (They should be fairly stiff.) Let cool slightly.
Cut cheese into 1" cubes. Place melted butter in a shallow bowl, and bread crumbs in another shallow bowl.
Shape about 1/4 cup of mashed potatoes around each cheese cube. Roll in melted butter, then crumbs.
Place each potato ball in a greased muffin cup. Bake at 425° for about 15-20 minutes or till golden brown. Potatoes should be crunchy on the outside, the cheese should be melted on the inside.
Notes
Since potatoes are different sizes, you may end up with more or less potato balls.
You can use leftover mashed potatoes instead of making them. You will need about 4 cups.