Scrub the potatoes and remove any eyes, then chop them into quarters (or smaller)and place them in a large pot. (I don’t peel them because the skin is thin and where the nutrients are.) Fill the pot so the water is about an inch over the top of the potatoes and bring them to a boil. Cook them until they can be easily pierced with a fork. While they're cooking, melt the butter and set it aside.
When the potatoes are tender, drain them and immediately add the melted butter and mix it into the potatoes with a hand mixer. Then add the half and half, or whipping cream (or a mixture of both). If the potatoes aren't creamy enough, add additional half and half/whipping cream.
Mix until they reach a creamy consistency. Then add salt to taste and serve them with a little dollop of butter in the middle.
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