Progress [on The Last Supper] was steady but slow, as the artist worked on in his typical thoughtful and meditative way. He spent considerable time roaming the streets of Milan looking for suitable models for faces of the apostles. By 1497 the only part left to complete was the head of Judas. At that point, the prior of the convent became so impatient with Leonardo's slowness that he complained to the duke, who summoned the artist to hear his reasons for the delay. According to Vasari, Leonardo explained to the Moor that he was working on The Last Supper at least two hours a day, but that most of his work took place in his mind. He went on, slyly, to say that, if he did not find an appropriate model for Judas, he would give the villain the features of the petulant prior. Ludovico was so amused by Leonardo's reply that he instructed the prior to be patient and let Leonardo finish his work undisturbed.

The Science of Leonardo, Fritjof Capra, pages 95--96.