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 reads 165-170 degrees, about 4-5 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 chilled custard to ice cream maker and follow manufacturer's instructions.
Transfer ice cream to container; cover and freeze until firm, at least 4 hours.