Peel the potatoes. Cut them into chunks, then cover them with cold water in a very large pot. Bring to a boil, then simmer until very tender all the way through. Drain the potatoes, then put them back into the pot over VERY low heat to evaporate any excess liquid. This will dry the potatoes.
While the potatoes are drying, heat whole milk just until hot, but not boiling. A good rule of thumb is to use about 2/3 cup milk for every 2 to 3 pounds of potatoes. You can use a mixture of cream and milk, if desired. Add butter or margarine to the hot, dry potatoes, keeping them over very low heat. Mash with a hand masher until the butter is melted and the potatoes are very smooth.
With an electric mixer, beat the potatoes (with the pot still over low heat) as you add the hot milk, a little at a time, until the potatoes are the desired consistency. Scrape sides of the pot with a rubber spatula. Do not overbeat. Stop beating when they are creamy and fluffy. Add salt and white pepper to taste. The white pepper is used so that they are no "unsightly" black specks in the potatoes.