Heat the cream and half-and-half to boiling in a saucepan. (If using the herb sprig, heat it with the cream mixture to boiling and let steep 1 hour. Remove the sprig, then reheat the cream to boiling.)
Whisk the egg yolks until completely blended. Whisk in about
Strain the custard into a mixing bowl and place immediately in a larger bowl filled with ice water. Heat the honey over low heat until liquefied, then stir into the custard. Chill the custard well, preferably overnight in the refrigerator. Freeze in an ice cream maker according to the manufacturer’s instructions.