Peel and grate the potato, discard any liquid from the grated potato and add it to a mixing bowl.
Add the egg, mashed potato, self-raising flour, salt and white pepper to the grated potato and mix with a fork.
Slowly add in the milk until a quite thick but spoonable batter is formed.
It should be "drop scone" texture, and form a nice mound on a spoon, but it will want to "drop off" the sides.
Heat the butter in a 30cm or 12" frying pan, over a medium-high heat, until it begins to brown, which should take 2-3 minutes.
Add a heaped dessertspoon or two of the boxty batter to the pan and cook for 3-4 minutes or until the top begins to bubble and set at the edges. Then flip and cook the second side for 2-3 minutes.