Place the bowl of your ice cream maker in the freezer overnight.
Whisk the yolks and sugar together until pale yellow.
Warm the milk and vanilla until it just lightly simmers.
Temper the egg/sugar mixture with the milk/vanilla mixture.
Return to the sauce pan and cook until thickened, stirring slowly and constantly. It should get to 170F.
Remove from heat. Add the tea leaves or bags to the pan. Stir. Steep for 30 minutes with the lid on.
Strain. Add the cream. Stir to combine.
Chill in the refrigerator ideally overnight, minimum 4 hours.
The next day, add your chilled ice cream to your ice cream maker. Churn (stir setting) until it is the thickness of soft serve ice cream, 20-25 minutes. You can enjoy it now as soft serve, or continue to final step for ice cream consistency.
Transfer to a container you can freeze and freeze at least 4 hours.
If you cannot wait to chill the ice cream before churning it, you can chill it quickly over a bowl filled with ice water. Just stir the ice cream to cool the base faster than your refrigerator can.