Place unpeeled potatoes in a large pot and cover with cold water. Generously season the water with salt and bring it to a boil. Cook for 25-35 minutes until the potatoes are fork-tender.
Drain the potatoes and cool them until they can be handled. Peel the potatoes and pass them through a potato ricer into a large mixing bowl. Alternatively, the potatoes may be mashed with a potato masher, but the texture may not be as smooth.
Add the egg yolk, fresh parsley, parmesan, and cubed mozzarella to the potatoes. Mix well to combine
Shape the mixture into 8 oval croquettes. Arrange the croquettes on a small baking sheet lined with parchment paper. Place in the refrigerator for 30 minutes.
Prepare a breading station by beating two eggs in a shallow dish and placing the breadcrumbs in a second shallow dish. Season both generously with salt and pepper to taste
Remove the croquettes from the fridge and roll each one into the beaten egg, letting any excess egg drip off before dredging in the breadcrumbs. Press lightly so that the breadcrumbs stick to the croquettes.
In a medium saucepan, heat one inch of vegetable oil to 350°F/180°C.
Fry the croquettes, a few at a time, in the hot oil for 3-4 minutes, turning with a spatula or tongs until golden brown and crisp on all sides. Do not crowd the oil. Allow the oil to return to 350˚F/180°C before adding the next batch of croquettes.
Remove from oil as they are ready and place on a paper towel to absorb excess oil.
Serve immediately with desired dipping sauces. Enjoy!