1. To a large saucepan, add potatoes and cover with cold water by a few inches, salt heavily. Transfer saucepan to stove sit sides dium-high heat, and bring to a simmer, monitoring heat to keep water at a simmer. Cook until a paring knife very easily slides through potatoes, 20-25 minutes. Drain and let cool slightly.
2. While potatoes are cooking, add butter to a medium skillet set over medium-high heat. Cook, stiring frequently with a wooden spoon to scrape up any browned bits, until butter stops foaming and takes on a golden-brown color, 5 to 7 minutes.
3. Meanwhile, to a small saucepan set over medium heat add heavy cream and milk, heat just hot; tum off heat.
4. When potatoes are tender enough to mash, drain thoroughly in a colander. Place saucepan back over medium heat. Add cooked potatoes and toss to dry completely; reserve pan again. Remove hot potatoes and immediately process in a potato ricer or food mill into a large bowl. Return processed potatoes to pan and set over low heat.
5. Drizzle hot cream mixture slowly into potato mixture, mixing constantly with a wooden spoon, until potatoes reach desired consistency. Gently fold in brown butter and mix potatoes by hand until just incorporated. Taste and adjust seasoning with salt and pepper.
6. To serve: Place potatoes in a large warmed serving bowl and top with chives; serve immediately.
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