Make clarified butter: Melt the butter in a small saucepan over low heat and cook until the white milk solids separate and rise to the top, about 3 minutes. Turn off the heat and carefully skim off the milk solids with a spoon; discard. Strain the remaining butter through a fine-mesh sieve and set aside (you should have about 1/4 cup clarified butter).
Peel the potatoes and grate them on the large holes of a box grater into a colander. Squeeze out the excess moisture with your hands, then blot the potatoes dry with paper towels.
Heat the clarified butter in a large nonstick skillet over medium-high heat. Add the potatoes to the skillet in a few piles and flatten with a spatula; sprinkle with 1 teaspoon salt, a few grinds of pepper and the paprika. Cook, undisturbed, until the potatoes start browning on the bottom, about 5 minutes. Flip, then drizzle with the cream; cook, undisturbed, until absorbed, about 2 minutes. Continue cooking, flipping the hash browns occasionally, until golden brown and crisp all over, about 15 more minutes. Season with salt and pepper.
Photograph by Ralph Smith
Courtesy of Food Network Magazine