Peel half of the potatoes and cut into 1-inch pieces.
Place them into a medium saucepan, cover with salted water by an inch, then bring to a simmer.
Cook until the potatoes are tender, about 15 minutes.
Drain the cooked potatoes and mash until smooth, then place into a large mixing bowl.
Meanwhile, as those potatoes are cooking, preheat oven to 200°F degrees.
Peel the remaining potatoes and grate with a box grater.
Wrap the raw grated potatoes in a kitchen towel and squeeze out as much liquid as possible.
Add the grated potatoes to the bowl with the mashed potatoes.
Add the flour, salt, baking powder, pepper, milk, and egg, stirring until incorporated.
Heat a large heavy skillet over medium heat until hot, then melt half the butter.
Cooking in small batches, add the batter ½ cup at a time, flattening the boxties with a spatula.
Turn them occasionally, and cook until golden, about 8 minutes per batch. Make sure you get the edges browned and crispy because they are delicious!
Place cooked boxties on a baking sheet in the preheated oven to keep warm as you repeat with the remaining patties, adding butter to the pan as needed.