In a large saucepan, simmer milk over medium heat. Remove from heat.
Stir in tea leaves and cover. Let steep 20 minutes.
In a medium bowl, whisk 4 egg yolks; set aside.
Strain milk twice through a fine mesh strainer. Remove as much of the tea leaves as possible.
Return milk to saucepan. Add sugar and heat until warm.
Place one tablespoon warmed milk mixture into egg yolks and stir. Repeat twice to temper yolks. Pour tempered yolks into milk.
Heat over medium heat, stirring constantly until the mixture covers the back of a spoon and reaches a food safe temperature of 160° F. Do not allow mixture to boil. Remove from the heat.
Strain the mixture into a bowl. Add cream. Cover bowl and allow it to stand out for 30 minutes.
Refrigerate until chilled. Once chilled, add mixture to the frozen bowl of an ice cream maker and follow the manufacturer’s directions.