Whisk yolks and sugar in medium bowl until thick, about 2 minutes. Heat milk and cream in medium saucepan over medium heat until mixture bubbles at edges.
Gradually whisk hot milk mixture into yolk mixture; return to saucepan. Stir over medium heat until custard leaves path on back of spoon when finger is drawn across and temperature registers 170°F, about 6 minutes.
Immediately pour custard through sieve set over another medium bowl. Stir Marsala, rum, and vanilla into custard. Cover; refrigerate at least 3 hours.
Process custard in ice cream maker. Transfer gelato to container. Cover and freeze until firm, at least 6 hours. (Can be made 2 days ahead. Keep frozen.).