Place the diced potatoes into a large pot and fill it with enough water to cover the potatoes. Place the pot on medium-high heat and bring the water to a boil. Once boiling, reduce the heat to a simmer.
Switch the stand mixer to medium speed and whip the potatoes until they are just smooth. Gradually add the remaining milk as needed. Be cautious not to overwhip the potatoes, as this can make them gluey.