Bring half-and-half with lemon and orange zests and cinnamon stick just to a boil over moderate heat. Cover and let stand off heat 25 minutes, then reheat to a simmer. Discard zests and cinnamon stick.
Whisk together yolks, sugar, and Sherry in a large bowl until smooth. Gradually whisk in hot milk mixture. Transfer custard to cleaned saucepan and cook over moderately low heat, stirring constantly, until thickened enough to coat back of a wooden spoon and an instant-read thermometer registers 170°F.
Pour custard through a fine sieve into a bowl and cover surface with wax paper to prevent a skin from forming. Chill until thoroughly cold, about 3 hours. Freeze in an ice-cream maker. Transfer to an airtight container and freeze until firm.
Bring figs, Sherry, juice, and honey, covered, to a boil in a small saucepan. Simmer, covered, just until figs are tender, about 40 minutes, then uncover and simmer until liquid is reduced to about 1 cup, about 8 minutes. Cool figs in syrup.
