1. Prepare the Vegetables: Grate the potatoes and carrots. To prevent the potatoes from turning brown, soak them in cold water, then drain and squeeze out excess moisture using a clean kitchen towel or cheesecloth. Finely chop the onion and mince the garlic.

2. Combine the Ingredients: In a large bowl, mix the grated potatoes, carrot, onion, and garlic. Add the grated cheese, crack in the egg, and sprinkle the flour. Season with salt and pepper, and mix everything until well combined.

3. Heat the Oil: In a large skillet, heat enough oil to coat the bottom of the pan over medium heat. Make sure the oil is hot before adding the batter to ensure a crispy crust.

4. Fry the Pancakes: Scoop small portions of the mixture into the skillet, flattening them slightly with the back of a spoon. Cook each pancake for 3-4 minutes on each side until golden brown and crispy.

5. Drain and Serve: Transfer the cooked pancakes to a plate lined with paper towels to remove excess oil. Serve hot with sour cream, applesauce, or your favorite dipping sauce.