In a medium bowl, whisk the egg yolks, set aside.
In a medium saucepan over medium heat, whisk the cream and milk. Stir constantly throughout the entire process to prevent scalding. Do not allow cream mixture to boil- only lightly simmer.
Add loose tea, and steep for 5 minutes, still continuing to stir.
Remove from heat. Run warm cream mixture through a fine sieve to remove loose tea. Place mixture back on stove immediately. Add honey. Stir.
Using a ladle, spoon about ¼ cup of warm, steeped cream into the egg yolks and whisk quickly to temper the yolks.
Slowly pour the bowl of tempered yolks into the warm cream, whisking vigorously as to prevent eggs from cooking when hitting the heat. Continue to stir constantly, until the custard is thick enough to coat the back of a spoon.
Remove from heat. Whisk in the vanilla and salt.
Transfer the mixture to a bowl or container and cover with a lid or plastic wrap. Chill completely in the refrigerator for at least 4 hours or overnight. Alternatively, you can freeze for at least 45 minutes for a fast chill prior to freezing.
Churn the ice cream in an ice cream machine according to the manufacturer's instructions. Transfer the mixture to a freezer-safe container, cover, and freeze until firm.