Peel the potatoes and rinse under cold water.
Cut each into quarters and place in a 3- to 4-quart saucepan.
Cover with cold water, partially cover the pot, and bring the water to a boil.
Uncover, add the 1 teaspoon of salt, and reduce the heat so that the water boils gently.
Cook until the potatoes are tender when pierced with a fork, about 10 to 12 minutes.
Meanwhile, in a small saucepan, heat the milk and butter together until the butter has melted and the mixture is hot but not boiling.
Drain the potatoes and return them to the warm pan over low heat for 1 minute to evaporate any excess water.
Use a potato masher, ricer, or food mill to mash the potatoes.
Stir the milk and butter mixture into the potatoes, a little at a time, until the potatoes are as soft and moist as you like.
Add salt and pepper to taste.