In a small food processor, combine the butter with the miso, lemon juice, and 1 tablespoon of water and pur?e until evenly combined.
In a 4-qt. saucepan, cover the sweet potatoes with water and bring to a boil. Reduce the heat to maintain a simmer and cook until the potatoes are soft, about 40 minutes. Drain the potatoes and transfer to a serving plate. Halve the potatoes lengthwise, drizzle the flesh with miso butter, and garnish with chives.