Fig.: to be almost completely deaf or pretend to be. Mainly used to mock someone

I've already told you and I'll say it again: you can't take my car because I need it for work. You must be deaf as a doornail!

Te l'ho già detto e ripetuto: non puoi prendere la mia macchina perché mi serve per lavoro. Hai forse le orecchie foderate di prosciutto?

This expression, although far less common than “dead as a doornail”, has its roots in old English literature. In 1546, Sir Thomas Urquhart published his translation of François Rabelais' book “Gargantua and Pantagruel”. In Book III, Chapter 3, XXXIV – How Women Ordinarily Have The Greatest Longing After Things Prohibited.” we find the lines:
… His wife perceiving that indeed he was as deaf as a door-nail, and that her scolding was but in vain, sith that he heard her not, she grew stark mad.