Begin by peeling the russet potatoes. Cut them into even-sized pieces to ensure uniform cooking. Then, boil them in salted water until they are fork-tender, which should take about 15-20 minutes. Drain and let them cool for a few minutes.
In a large mixing bowl, mash the boiled potatoes until smooth. Make sure there are no lumps! Stir in the cornstarch, salt, and shredded mozzarella cheese. Mix until everything is well combined and a dough-like consistency forms.
Take small portions of the potato mixture and roll them into sticks, about the size of your pinky finger. Make sure they are compact, so they hold their shape while frying.
In a large saucepan, heat enough vegetable oil over medium-high heat. You want the oil to be hot enough for frying but not smoking. A good way to test this is to drop a small piece of the potato mixture into the oil; it should sizzle immediately.
Carefully place a few potato sticks into the hot oil, making sure not to overcrowd the pan. Fry them for about 3-4 minutes on each side or until they are golden brown and crispy. Use a slotted spoon to remove them, and place them on a paper towel-lined plate to drain excess oil.
Once all the potato cheese sticks are fried, sprinkle them with grated parmesan cheese and chopped fresh parsley for a burst of flavor. Serve them hot with your favorite dipping sauce, such as marinara or ranch, and enjoy!