1. In a medium saucepan over medium-low heat, bring milk and cream to a simmer. Remove from heat. Stir in green tea leaves and let stand for 10 minutes.
2. In a bowl, whisk egg yolks with sugar until thickened and pale yellow. Whisk in cornstarch. Gradually whisk in cream mixture.
3. Return entire mixture to the saucepan. Cook over low heat, stirring constantly, until the mixture is thick enough to coat the back of a wooden spoon. Be careful not to let it boil. Strain into a clean large bowl. Let cool to room temperature. Cover and refrigerate until completely cold or overnight.
4. Stir cream mixture. Transfer to an ice cream maker and freeze according to manufacturer's instructions.