1 Heat the oven to 200°F.
2 Chop half of the potatoes into large dice, place in a medium saucepan, salt generously, and cover with cold water by 1 inch. Bring to a boil over high heat, reduce the heat to low, and simmer the potatoes uncovered until fork tender, about 8 minutes.
3 Meanwhile, grate the remaining potatoes on the large holes of a box grater. Toss with 1/4 teaspoon of the salt and place in a fine mesh strainer set over a medium bowl; set aside.
4 When the boiled potatoes are ready, drain them, return them to the pot, add 1/4 cup of the milk, and mash until the potatoes are smooth.
5 With a plastic spatula, press the grated potatoes against the sides and bottom of the strainer to remove any liquid. Add the grated potatoes to the mashed potatoes (no need to stir though).
6 Place the egg, remaining 1/2 cup milk, flour, pepper, and remaining 1 teaspoon salt in a large bowl and whisk until smooth, about 10 seconds. Add the potatoes and stir until evenly incorporated.
7 Heat a large nonstick frying pan or griddle over medium heat. Test to see if the pan is hot enough by sprinkling a couple of drops of cold water in it: If the water bounces and sputters, the pan is ready to use; if it evaporates instantly, the pan is too hot.
8 Once the pan is ready, add enough butter to lightly coat the bottom when melted. Drop 3 dollops (about 1/4 cup each) of the batter into the pan and spread each to about 1/4 inch thick. Cook until the pancake bottoms are golden brown, about 4 to 5 minutes. Flip and cook the other side until golden brown, about 4 to 5 minutes more. Place on a baking sheet and set in the oven to keep warm. Repeat with the remaining butter and batter. Serve warm.