Depending on size, boil the potatoes for about 20-25 minutes. Insert a knife; the potatoes are ready if it goes smoothly without resistance. Choose a starchy variety with a slightly floury texture and low moisture content to prevent them from falling apart while boiling. (Many brands already tell you in the packaging if they are good to boil)
Peel the potatoes, place them in a bowl, and mash them as if you were making mashed potatoes, using a potato masher, a food mill, or even a fork, but never a food processor for this recipe. A blender or food processor could make the potatoes too mushy or soft. Let them cool.
Add the egg yolk, freshly ground pepper, grated Parmesan cheese, a bit of chopped fresh parsley, and salt, and mix until smooth.
Dampen your hands and shape the croquettes into balls or, better yet, into the traditional elongated "log" shape.
Cut the cheese into thin sticks for the filling. Italian stringy cheeses like mozzarella, provolone, or scamorza are the best for this recipe.
Make a longitudinal cut in the croquette, insert a cheese stick into the slit, and then close it again. If you're using square cheese pieces instead of sticks, you can carefully insert two or three cubes into each croquette and then close it again so that the outer surface of the croquette is smooth again.
Bread coating: Beat two eggs lightly and coat the croquettes before rolling them in the breadcrumbs.
Fry the croquettes in a pan or skillet with vegetable oil and place them on a dish after you drain the excess oil.