Fill a large pot 3/4 of the way full with water. Bring to a boil over high heat. While the water boils, peel the potatoes, rinse them, and cut each potato into 1/2-inch cubes.
Add the potato cubes to the boiling water. Once the water returns to a boil, reduce the heat to medium-high. Stir the potatoes occasionally and cook until fork tender, about 20 minutes.
Drain the potatoes and return to the pot. Add the butter and use a potato masher to break up the potatoes and incorporate the butter.
Pour in half of the milk, and use the potato masher to incorporate the milk into the potatoes. (You want the potatoes mostly smooth with some small lumps.)
Pour in the rest of the milk and use a wooden spoon to incorporate the milk into the potatoes until smooth. (see note)
Season with salt and pepper and mix to combine. Cover to keep warm or serve immediately.
Notes
You're welcome to add a little more milk if you feel your potatoes aren't creamy/smooth enough. Season the potatoes to taste. The salt and pepper amounts listed are how I like my potatoes.