Pour the buttermilk into a separate container and reserve for another use. Place the butterball in the empty bowl. Be sure to squeeze out all excess butter from the cheesecloth. Pour 1/3 cup of ice water over the butter and, using a spatula, “wash” the butter, folding it over itself and pressing down to extract the extra buttermilk. Drain off the milky liquid and discard it; repeat this process until the liquid is clear, 4 to 6 times. The butter will start to harden; at that point your hands may work better than the spatula.