Mix the heavy cream, half and half, vanilla bean, rosemary, sugar, and salt in a heavy saucepan. Heat slowly over low heat, stirring often until sugar is dissolved.
Once the sugar is dissolved turn heat up to medium and bring mixture to a gentle simmer for one minute. Remove from heat. Strain out vanilla bean and rosemary.
Whisk egg yolks in a separate bowl. Slowly whisk the hot mixture to the yolks until they are fully tempered. Return yolk mixture to the saucepan and continue to cook over low heat stirring constantly until mixture is thickened like a thin custard.
Transfer to a glass container and chill in refrigerator at least 6 hours. Freeze in ice cream maker according to machine instructions.