In a 3- to 4-quart pan over high heat, stir chai tea and sugar until boiling. Remove from heat. Whisk in chocolate, cover, and let stand 10 minutes. Uncover; whisk to combine. Whisk in half-and-half and the cinnamon, cardamom, and cloves. Cover and chill until cold, at least 3 hours or up to 1 day.
Freeze in an ice cream maker (at least 1 1/2-qt. capacity) according to manufacturer's instructions until machine stops or dasher is hard to turn. Transfer sorbet to an airtight container and freeze until firm, about 3 hours.