Start by peeling the sweet potatoes. Once peeled, grate them using a box grater or a food processor. Place the grated sweet potatoes in a clean kitchen towel or cheesecloth and squeeze out as much excess moisture as possible.
In a large mixing bowl, combine the grated sweet potatoes, eggs, grated Parmesan, chopped parsley, salt, and pepper. Mix everything together until well combined.
In a skillet, add enough vegetable oil to cover the bottom of the pan generously. Heat the oil over medium-high heat until it shimmers.
Using your hands, take a small handful of the sweet potato mixture and shape it into a patty. Carefully place it in the hot oil. Repeat with the remaining mixture.
Fry the hash browns for about 4-5 minutes on each side or until they turn golden brown and crispy. Use a spatula to flip them gently.
Once cooked, transfer the hash browns to a plate lined with paper towels to drain any excess oil. Serve immediately.