You can peel the potatoes ahead of time, but I prefer to boil the large chunks of potatoes with their skin on in boiling salted water until very tender, about 20 minutes. Then I drain the potatoes and when they're cool enough to handle, the peels slip right off.
To make the brown butter, add the butter to a small sauce pan. Heat over medium heat. The butter will at first melt, then little brown bits will form on the bottom of the pan and it will start to smell wonderfully nutty. Whisk the butter as it melts to ensure even heating. When the butter is browned but not burnt, its done.
Mash the potatoes with the buttermilk, salt and pepper, and half of the browned butter reserving the other half to pour over the top.
Arrange the potatoes on a serving platter or in a serving bowl and add remaining browned butter as well as fresh chives as garnish.