Preheat the oven to 425 degrees F. Grease four 10-ounce ramekins with the butter and place on a rimmed baking sheet.
Place the potatoes in a large pot and cover with cold water. Season the water generously with salt and bring to a boil over high heat. Lower the heat to medium and simmer until the potatoes are tender when pierced with a knife, about 10 minutes.
Meanwhile, heat the milk and cream in a medium saucepan over medium heat until small bubbles appear around the edges, 2 to 3 minutes. Slowly add the American cheese, stirring until melted. Remove from the heat.
Drain the potatoes well and return to the pot. Place over low heat, stirring constantly, until the excess water evaporates, about 1 minute. Mash the potatoes with a potato masher, leaving a few clumps of potato. Slowly pour in the milk and cheese mixture and 1/4 cup of the Parmesan, mix to combine. Taste and adjust seasoning.
Divide the potatoes evenly between the prepared ramekins. Top each with 1 tablespoon of the remaining Parmesan. Bake until the top is golden brown and the edges are bubbling, about 15 minutes. Garnish with the chives and serve.
Copyright 2020 Television Food Network, G.P. All rights reserved.