Combine the potatoes and garlic in a saucepot and cover by 4 inches with cold water. Add the salt and bring the pot to a simmer. Simmer until completely tender, about 25 minutes. When done, the potato pieces should be easily crushed with the back of a spoon. Strain the potatoes and leave to drain and steam dry in the colander for 2 to 3 minutes.
While the potatoes drain, combine the milk and butter in a small saucepot and bring to a simmer over low heat.
Transfer the potatoes to a bowl and mix on low with an electric mixer. When the potatoes are broken into small pieces, add the milk in several additions and continue mixing on low until incorporated. Turn the mixer to high and whip until silky and smooth. Add more warm milk if necessary. Season to taste with salt and pepper. Transfer to a serving bowl and sprinkle with parsley, if desired.