In a large pot, bring 3 quarts of water and the salt to a boil. Meanwhile, peel and rinse the potatoes. Cut each potato in half, cut each of the halves in half again (quarters) and then once more into eighths. Carefully add the potatoes to the pot. It helps to gently tip them in from a colander or bowl so you don't get splashed by boiling water.

Bring the water back to a boil over high heat, about 4-5 minutes. Depending on the size of your pot, the water might bubble over when it reaches a boil again. Keep an eye on it until it's boiling, and then turn it down to medium-high heat. Cook at a low boil over medium-high heat until tender (check with a fork), about 10-15 minutes.

When the potatoes are tender, carefully and gently drain them into a colander over the sink. Leave them in the colander while you warm the other ingredients in the pot.

Over low heat, add butter, sour cream and half and half to the pot. Stir well to combine, until the butter melts. Turn off the heat, gently add the potatoes back to the pot, and mash them with a potato masher until smooth (add a little milk if they are still too thick).