Place the potatoes in a large pot, then add enough cold water to cover them by 1 inch. Add a generous spoonful of salt, then cover the pot and bring to a boil over high heat. Set the lid ajar and reduce the heat to medium-low. Cook the potatoes at a steady simmer until they are barely tender when pierced with the tip of a small, sharp knife, 20 to 25 minutes. Drain the potatoes well.
Return the potatoes to the pot. Cook them over medium-low heat, stirring almost constantly, until the potatoes begin to film the bottom of the pot, about 3 minutes. Add the cream cheese. Using a handheld electric mixer, whip the potatoes until the cream cheese melts. Add the sour cream, milk and the 6 tablespoons room temperature butter. Mix well. Season to taste with salt and pepper.
Use a bit of butter to lightly coat a 13-by-9-inch baking dish. Transfer the potatoes to the baking dish, smoothing the top. Dot the top of the casserole with the 2 tablespoons of cubed butter. Let cool completely. Cover with plastic wrap and refrigerate for up to 1 day. Remove from the refrigerator 1 hour before the final baking.