Add cubed potatoes to large pot, then fill pot with enough water to fully cover potatoes. Waterline should sit approximately 1-inch above top of potatoes. Salt water with 1 large pinch salt.
Heat pot over high heat. When water begins to boil, reduce heat to medium and simmer 20 minutes or until potatoes are very tender. Use fork to check doneness - tines of fork should pierce potatoes with no resistance.
Carefully pour water and potatoes out of pot and into colander. Drain well, then transfer potatoes to large mixing bowl. Use potato masher to lightly mash potatoes.
Preheat oven to 350° Fahrenheit. Place butter in small, microwave-safe bowl. Microwave 30 seconds or until butter is melted but not bubbling or burnt.
Add melted butter, cream cheese, milk, sour cream, and ½ cup shredded cheddar to mixing bowl with potatoes. Resume mashing until potato mixture is light and fluffy, being careful not to overwork potatoes. Taste potato mixture and add salt if desired.
Transfer mashed potato mixture to baking dish. Spread potatoes out to cover bottom of dish evenly and smooth top of potatoes. Sprinkle remaining cheddar cheese over top of potatoes, then cover dish with aluminum foil.
Place baking dish in preheated oven and bake potatoes, covered, 30 minutes. After 30 minutes, carefully remove foil and return dish to oven, baking potatoes another 10 minutes or until cheese on top is melted and bubbly.
Carefully remove baking dish from oven. Let stand 5 minutes then serve warm.