Preheat your oven to 350°F and lightly butter a 2-quart rectangular baking dish.
Steam the potato cubes in a large steamer basket over boiling water until they are very tender (about 25 to 30 minutes).
In a large bowl, mash the steamed potatoes with butter, salt, and pepper until nearly smooth. Gradually mix in the milk, half of the shredded cheese, crisp bacon, sour cream, and chives until well combined.
Transfer the potato mixture into the prepared baking dish, spreading it evenly. Top with the remaining shredded cheese.