Peel and grate the raw potatoes using a box grater or food processor. Place the grated potatoes in a clean kitchen towel and squeeze out excess moisture. In a separate bowl, mash your cooked potatoes until smooth.
In a large mixing bowl, combine the grated raw potatoes, mashed potatoes, flour, baking powder, salt, pepper, egg, and milk. Mix until all ingredients are well combined. The batter should be thick but pourable; adjust the milk as needed.
Heat a large skillet or frying pan over medium heat and add a tablespoon of butter or oil.
Pour about 1/4 cup of the batter into the pan for each pancake. Flatten slightly with the back of a spatula. Cook for 4-5 minutes on each side or until golden brown and crispy. Repeat with the remaining batter, adding more butter or oil as needed.
Once cooked, transfer the Boxty to a plate lined with paper towels to absorb excess oil. Serve warm with your choice of toppings, such as sour cream, chives, smoked salmon, or applesauce.