Peel potatoes and cut into quarters. Transfer to a bowl of cold water and rinse to remove starch. Drain and transfer to a pot of cold water. Very generously salt the water and bring to a boil over high heat. Reduce heat and simmer until potatoes are soft and the tip of a knife goes in easily, 20 to 25 minutes.

While the potatoes are cooking, cut butter in chunks and let come to room temperature.

Drain potatoes thoroughly and return to the pot. Set over medium-low heat and mash with a potato masher until potatoes. Season with salt and pepper and add 1/4 of the softened butter chunks. Mash until butter just about disappears.

Add another 1/4 of the butter and mix with a wire whisk until it just about disappears. Whisk in the remaining quarters of butter in 2 additions as before; potatoes will be light and creamy after all the butter has been mixed in.

Whisk in hot milk until incorporated. Add cayenne and more salt if needed.
Garnish with chives.
Serve immediately.