pudding-sleeve noun1 •A large bulging sleeve, like that of the English clergy's gown.His grazier's coat fall dovvn his heels: / He sees, yet hardly can believe, / About each arm a pudding-sleeve; / His vvaistcoat to a cassock grevv / And both assum'd a sable hue — 1708 formspudding sleeves · pudding-sleeves