In a saucepan, combine the heavy cream, whole milk, and sugar. Heat over medium heat until the sugar is dissolved and the mixture is hot, but not boiling.
Add the Thai tea bags to the hot cream mixture. Remove from heat and let steep for 30 minutes.
Remove the tea bags and reheat the mixture until hot again.
In a mixing bowl, whisk the egg yolks. Slowly pour the hot cream mixture into the yolks, whisking constantly to temper the eggs.
Return the mixture to the saucepan and cook over low heat, stirring constantly, until the mixture thickens and coats the back of a spoon.
Strain the mixture through a fine-mesh sieve into a clean bowl. Let cool to room temperature, then cover and refrigerate until completely chilled, at least 4 hours or overnight.
Churn the chilled mixture in an ice cream maker according to the manufacturer's instructions. Transfer to a container and freeze until firm, about 2 hours.