Combine cream, milk, honey, and rosemary in large saucepan. Stir over medium heat until small bubbles form around edges of pan (scalding). Remove from heat; cover and let steep 30 minutes. Discard rosemary. Return cream mixture to simmer; remove from heat.
Whisk yolks and sea salt in medium bowl. Gradually add hot cream mixture; whisk until blended. Return custard to same saucepan and stir over medium-low heat until custard thickens slightly and coats back of spoon when finger is drawn across and instant-read thermometer inserted into custard registers 165°F to 170°F, 4 to 5 minutes (do not boil). Strain into medium bowl. Set bowl over larger bowl filled with ice and water; stir occasionally until cool, about 10 minutes. Stir in vanilla extract. Remove bowl from ice and water. Cover custard with plastic wrap and chill at least 4 hours or overnight.
Transfer custard to ice cream maker and follow manufacturer's instructions. Transfer ice cream to container; cover and freeze until firm, at least 4 hours. Can be made 4 days ahead. Keep frozen.