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.