Step 1Peel the potatoes and cut them into 1 1/2 -inch pieces. Place them in a 4-quart saucepan and add water to cover the potatoes by 2 inches. Add 1 teaspoon salt and bring to a boil over high heat. Reduce the heat to medium-high and cook until the potatoes are tender, 15 to 20 minutes.
Step 2While the potatoes are cooking, heat the butter in a heavy 9-inch skillet over medium-heat until melted. Once the butter has melted, whisk until it turns golden brown, about 4 to 5 minutes. Set aside.
Step 3When the potatoes are tender, drain well. Put the potatoes through a potato ricer or mash the potatoes. Sprinkle over three-fourths teaspoon salt and one-eighth teaspoon pepper. Set aside 2 tablespoons of the brown butter to drizzle over the top. Add the remaining brown butter to the potatoes along with the warm milk. Lightly stir just to combine, being careful not to overmix.
Step 4Spoon the potatoes into a serving bowl. Drizzle over the remaining 2 tablespoons butter and sprinkle with chives.