Peel the potatoes, and cut them into 1-inch dice. Place the potatoes and 1/2 teaspoon kosher salt in a small saucepan, and cover with water. Place over high heat. When water comes to a boil, reduce heat just enough to maintain a heavy simmer. Cook 12-15 minutes, or until the potatoes are so tender they come apart when prodded with a fork. Once potatoes are fully cooked: remove and reserve about 1/2 cup cooking liquid, then drain the potatoes well. Place the drained but still hot potatoes in a mixing bowl. Using a potato masher, mash the potatoes until smooth. Stir in 1 pat butter. Stir in just enough of the reserved cooking liquid to bring the potatoes to your desired consistency. Taste and adjust seasoning as desired. Cover to keep warm.