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Bring a pot of salted water to a boil. Add the potatoes once the water comes to a boil.
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Cook the potatoes for 15 minutes, or until soft.
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Drain the potatoes and pour them into a bowl.
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Melt the butter in a small saucepan over medium low heat. The butter will simmer, bubbling steadily. Stir frequently, and the butter will brown very quickly. As soon as it begins to brown, turn the heat off. The butter will continue to brown.
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Add the butter, pecorino, cream, broth, and half of the salt and pepper to the potatoes. Mash the potatoes with a fork or potato masher. Taste test, and add more salt and pepper based on your preferences. Add more broth if the potatoes need more moisture.