Boil the potatoes in lightly salted water until tender. Meanwhile, melt the butter in a small skillet set over medium heat. Add the leeks and cook for 3 to 4 minutes. Add the stock, bring to a simmer and cook until the stock has almost evaporated and the leeks are very tender, about 4 to 5 minutes.
Remove from the heat and set aside. When the potatoes are tender, drain well and mash. Mix in the buttermilk, reserved leeks, and salt and pepper. Serve immediately.