Peel the eggs and separate the yolks from the whites. Save the whites for another use. Press the egg yolks through a fine-mesh strainer so that they become mashed and powdery. Place in a large bowl with butter, confectioners’ sugar, milk, vanilla, nutmeg, cloves, and salt. Beat together until smooth, then raise mixer speed and beat until mixture is thick and frosting-like, about three minutes. Stir in the rum by hand, if using.