Begin by peeling and chopping the potatoes into even chunks. Place them in a pot of salted water and bring to a boil. Cook until fork-tender, then drain and mash smooth. Allow to cool.

In a large bowl, combine the cooled mashed potatoes, shredded cheese, flour, beaten egg, and seasonings. Mix thoroughly until a uniform dough-like consistency forms.

Lightly flour your hands and form the mixture into sticks or logs about 4-6 inches long and 1 inch thick. Place on a baking sheet lined with parchment paper.

Roll each stick in breadcrumbs if desired. Heat oil in a skillet to 350°F (175°C). Fry in small batches until golden brown and crispy, about 3-4 minutes.

Remove sticks with a slotted spoon and place on paper towels to drain excess oil. Serve warm with your favorite dipping sauce.