Put potatoes in a large pot with enough water to cover them by a couple of inches, generously salted. Bring to a boil over medium-high hear, then reduce to medium-low and cook until the potatoes are tender, 20-30 minutes. Let drain and cool in a colander for five minutes, then run through a food mill.
Preheat oven to 400-450F.
Melt butter and cream in a small pan and heat until it just begins to bubble. Add the cream mixture into the potatoes and stir to combine. Add 3⁄4 of the chives and 3⁄4 of the cheese. Season with salt and pepper, and stir to combine. Spoon into two small cocottes or a casserole dish, and top with the rest of the cheese.
Bake until the cheese is lightly browned, 10-15 minutes. Let stand for 10 minutes, sprinkle with the rest of the chives and serve.
Two big servings or four small ones.